Robert S. Strichartz

Publication List       (updated 10/04)

(All papers available on request, by number. Asterisk (*) indicates works not in final form.)

Research Papers

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[R1]" Isometric isomorphisms of measure algebras, Pacific Journal of Mathematics, 15 (1965), 315-317.

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[R2]" Isomorphisms of group algebras, Proceedings of the American Mathematical Society, 17 (1966), 858-862.

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[R3]" Multipliers on fractional Sobolev spaces, Journal of Mathematics and Mechanics, 16 (1967), 1031-1060.

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[R4]" Sobolev inequalities and extension theorems for functions with certain L^p-derivatives, Studia Mathematica, 30 (1968), 1-15.

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[R5]" Fubini-type theorems, Annali della Scuola Normale Superiore di Pisa Classe di Scienze, XXII (1968), 399-408.

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[R6]" L^p estimates for integral transforms, Transactions of the American Mathematical Society, 136 (1969), 33-50.

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[R7]" A multilinear version of the Marcinkiewicz interpolation theorem, Proceedings of the American Mathematical Society, 21 (1969), 441-444.

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[R8]" Convolutions with kernels having singularities on a sphere, Transactions of the American Mathematical Society, 148 (1970), 461-471.

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[R9]" A priori estimates for the wave equation and some applications, Journal of Functional Analysis, 5 (1970), 218-235.

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[R10]" The stationary observer problem for \square u = Mu and related equations, Journal of Differential Equations, 9 (1971), 205-223.

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[R11]" A note on Sobolev algebras, Proceedings of the American Mathematical Society, 29 (1971), 205-207.

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[R12]" Invariant pseudo-differential operators on a Lie group, Annali della Scuola Normale Superiore di Pisa, 26 (1972), 587-611.

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[R13]" Multipliers for spherical harmonic expansions, Transactions of the American Mathematical Society, 167 (1972), 115-124.

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[R14]" A functional calculus for elliptic pseudo-differential operators, American Journal of Mathematics, 94 (1972), 711-722.

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[R15]" The Hardy space H¹ on manifolds and submanifolds, Canadian Journal of Mathematics, 24 (1972), 915-925.

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[R16]" A note on Trudinger's extension of Sobolev's inequalities, Indiana University Mathematical Journal, 21 (1972), 841-842.

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[R17]" Boundary values of solutions of elliptic equations satisfying H^p conditions, Transactions of the American Mathematical Society, 176 (1973), 445-462.

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[R18]" a. Harmonic analysis on hyperboloids, Journal of Functional Analysis, 12 (1973), 341-383.
b. (Informal summary of the above) A non-compact analogue of spherical harmonics, Proceedings of Symposia in Pure Mathematics, vol. 26, American Mathematical Society, Providence, 1973, 357-358.

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[R19]" Multiplier transformation on compact Lie groups and algebras, Transactions of the American Mathematical Society, 193 (1974), 99-110.

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[R20]" Fourier transforms and non-compact rotation groups, Indiana University Mathematical Journal, 24 (1974), 499-526. Errata 30 (1981), 479-480.

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[R21]" The explicit Fourier decomposition of L²(SO(n)/SO(n-m)), Canadian Journal of Mathematics, 27 (1975), 294-310.

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[R22]" Singular integrals on nilpotent Lie groups, Proceedings of American Mathematical Society, 53 (1975), 367-374.

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[R23]" Bochner identities for Fourier transforms, Transactions of the American Mathematical Society, 228 (1977), 307-327.

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[R24]" Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Journal of Mathematics, 44 (1977), 705-714.

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[R25]" Minimum energy solutions of certain underdetermined problems in partial differential equations, Journal of Differential Equations, 27 (1978), 64-91.

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[R26]" Bounded mean oscillation and Sobolev spaces, Indiana University Mathematics Journal, 29 (1980), 539-558.

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[R27]" Asymptotic behavior of waves, Journal of Functional Analysis, 40 (1981), 341-357.

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[R28]" Traces of BMO-Sobolev spaces, Proceedings American Mathematical Society, 83 (1981), 509-513.

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[R29]" L^p estimates for Radon transforms in Euclidean and non-Euclidean spaces, Duke Mathematical Journal, 48 (1981), 699-727.

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[R30]" Explicit solutions of Maxwell's equations on a space of constant curvature, Journal of Functional Analysis, 46 (1982), 58-87.

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[R31]" A Poisson summation formula for integrals over quadratic surfaces, Transactions American Mathematical Society, 270 (1982), 163-173.

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[R32]" Singular integrals supported on submanifolds, Studia Mathematica, 74 (1982), 137-151.

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[R33]" Compositions of singular integral operators, Journal of Functional Analysis, 49 (1982), 91-127.

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[R34]" Improved Sobolev inequalities, Transactions American Mathematical Society, 279 (1983), 397-409.

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[R35]" Analysis of the Laplacian on a complete Riemannian manifold, Journal of Functional Analysis, 52 (1983), 48-79.

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[R36]" Mean value properties of the Laplacian via spectral theorey, Transactions American Mathematical Society, 284 (1984), 219-228.

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[R37]" L^p contractive projections and the heat semi-group for differential forms, Journal of Functional Analysis, 65 (1985), 348-357.

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[R38]" Harmonic analysis on Grassmannian bundles, Transactions American Mathematical Society, 296 (1986), 387-409.

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[R39]" Sub-Riemannian geometry, Journal of Differential Geometry, 24 (1986), 221-263. Errata 30 (1989), 545-596.

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[R40]" The Campbell-Baker-Hausdorff Dynkin formula and solutions of differential equations, Journal of Functional Analysis, 72 (1987), 320-345.

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[R41]" Linear algebra of curvature tensors and their covariant derivatives, Canadian Journal of Mathematics, 40 (1988), 1105-1143.

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[R42]" Local harmonic analysis on spheres, Journal of Functional Analysis, 77 (1988), 403-433.

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[R43]" Uncertainty principles in harmonic analysis, Journal of Functional Analysis, 84 (1989), 97-114.

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[R44]" Harmonic analysis as spectral theory of Laplacians, Journal of Functional Analysis, 87 (1989), 51-148. Errata 109 (1992), 457-460.

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[R45]" Magnified curves on a flat torus, determination of almost periodic functions, and the Riemann-Lebesgue Lemma, Proceedings of the American Mathematical Society, 107 (1989), 755-759.

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[R46a]" Fourier asymptotics of fractal measures, Journal of Functional Analysis, 89 (1990), 154-187.

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[R46b]" Besicovitch meets Wiener - Fourier expansions and fractal measures, Bulletin of the American Mathematical Society, 20 (1989), 55-59.

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[R47]" H^p Sobolev spaces, Colloquium Mathematician, 60/61 (1990), 129-139.

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[R48]" Harmonic analysis on constant curvature surfaces with point singularities, Journal of Functional Analysis, 91 (1990), 37-116.

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[R49]" Self-similar measures and their Fourier transforms I, Indiana University Mathematics Journal, 39 (1990), 797-817.

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[R50]" L^p harmonic analysis and Radon transforms on the Heisenberg group, Journal of Functional Analysis, 96 (1991), 350-406.

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[R51]" Spectral asymptotics of fractal measures on Riemannian manifolds, Journal of Functional Analysis, 102 (1991), 176-205.

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[R52]" Wavelet expansions of fractal measures, Journal of Geometric Analysis, 1 (1991), 269-289.

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[R53]" Self-similarity on nilpotent Lie groups, Contemporary Mathematics, 140 (1992), 123-157.

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[R54]" (with Prem Janardhan and David Rosenblum) Numerical experiments in Fourier asymptotics of Cantor measures and wavelets, Experimental Mathematics, 1 (1992), 249-273.

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[R55]" Self-similar measures and their Fourier transforms II, Transactions of the American Mathematical Society, 336 (1993), 335-361.

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[R56]" Self-similar measures and their Fourier transforms III, Indiana University Mathematics Journal, 42 (1993), 367-411.

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[R57]" Wavelets and self-affine tilings, Constructive Approximation, 9 (1993), 327-346.

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[R58]" Complementary series and exotic Sobolev norms, Journal of Functional Analysis, 114 (1993), 493-508.

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[R59]" Characterization of eigenfunctions of the Laplacian by boundedness conditions, Transactions of the American Mathematical Society, 338 (1993), 971-979.

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[R60]" A fractal Radon inversion problem, Journal d'Analyse Mathématique, 64 (1994), 219-240.

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[R61]" (with Arthur Taylor and Tong Zhang) Densities of self-similar measures on the line, Experimental Mathematics, 4 (1995), 101-128.

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[R62]" Estimates for sums of eigenvalues for domains in homogeneous spaces, Journal of Functional Analysis, 137 (1996), 152-190.

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[R63]" (with Ron Dror and Suman Ganguli) A search for best constants in the Hardy-Littlewood maximal theorem, Journal of Fourier Analysis and Applications 2 (1996), 473-486.

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[R64]" (with David Glickenstein) Nonlinear self-similar measures and their Fourier transforms, Indiana University Mathematics Journal 45 (1996), 205-220.

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[R65]" Piecewise linear wavelets on Sierpinski gasket type fractals, Journal of Fourier Analysis and Applications, 3 (1997), 387-416.

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[R66]" Fractals in the large, Canadian Journal of Mathematics, 50 (1998), 638-657.

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[R67]" (with John-Peter Lund and Jade P. Vinson) Cauchy transforms of self-similar measures, Experimental Mathematics, 7 (1998), 177-190.

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[R68]" Remarks on ``Dense analytic subspaces in fractal L²-spaces'' by P. E. T. Jorgensen and S. Pedersen, Journal d'Analyse Mathématique 75 (1998), 229-231.

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[R69]" (with Elizabeth Ayer) Exact Hausdorff measure and intervals of maximal density for Cantor sets, Transactions American Mathematical Society 351 (1999), 3725-3741.

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[R70]" Isoperimetric estimates on Sierpinski gasket type fractals, Transactions American Mathematical Society 351 (1999), 1705-1752.

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[R71]" (with Kyallee Dalrymple and Jade P. Vinson) Fractal differential equations on the Sierpinski gasket, Journal of Fourier Analysis and Applications 5 (1999), 203-285.

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[R72]" (with Yang Wang) Geometry of self-affine tiles I, Indiana University Mathematics Journal 48 (1999), 1-23.

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[R73]" (with Richard Kenyon, Jie Li and Yang Wang) Geometry of self-affine tiles II, Indiana University Mathematics Journal 48 (1999), 25-42.

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[R74]" (with Oren Ben-Basset and Alexander Teplyaev) What is not in the domain of the Laplacian on Sierpinski gasket type fractals, Journal of Functional Analysis 166 (1999), 197-217.

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[R75]" Some properties of Laplacians on fractals, Journal of Functional Analysis 164 (1999), 181-208.

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[R76]" Taylor approximations on Sierpinski gasket type fractals, Journal of Functional Analysis, 174 (2000), 76-127.

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[R77]" (with Michael Usher) Splines on fractals, Mathematical Proceedings of the Cambridge Philosophical Society, 129 (2000), 331-360.

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[R78]" Gibbs' phenomenon and arclength, Journal of Fourier Analysis and Applications, 6 (2000), 533-536.

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[R79]" Mock Fourier series and transforms associated with certain Cantor measures, Journal d'Analyse Mathématique, 81 (2000), 209-238.

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[R80]" The shape of the error in wavelet approximation and piecewise linear interpolation, Mathematical Research Letters, 7 (2000), 317-327.

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[R81]" (with Jun Kigami and Daniel Sheldon) Green's functions on fractals, Fractals 8 (2000), 385-402.

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[R82]" The Laplacian on the Sierpinski gasket via the method of averages, Pacific Journal of Mathematics, 201 (2001), 241-256.

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[R83]" (with Michael Gibbons and Arjun Raj) The finite element method on the Sierpinski gasket, Constructive Approximation 17 (2001), 561-588.

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[R84]" (with Jun Kigami and Katharine C. Walker) Constructing a Laplacian on the diamond fractal, Experimental Mathematic, 10 (2001), 437-448.

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[R85]" (with Nina Huang) Sampling theory for functions with fractal spectrum, Experimental Mathematics 10 (2001), 619-638.

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[R86]" Harmonic mappings of the Sierpinski gasket to the circle, Proceedings American Mathematical Society 130 (2001), 805-817.

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[R87]" (with Anders Öberg and Andrew Q. Yingst) Level sets of harmonic functions on the Sierpinski gasket, Arkiv för Matematik, 40 (2002), 335-362.

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[R88]" (with Scott Bailey and Theodore Kim) Inside the Lévy dragon, American Mathematical Monthly, 109 (2002), 689-703.

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[R89]" (with Bryant Adams, S. Alex Smith and Alexander Teplyaev) The spectrum of the Laplacian on the pentagasket, Trends in Mathematics: Fractals in Graz 2001, Birkhauser (2003), 1-24.

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[R90]" (with Jeremy Stanley and Alexander Teplyaev) Energy partition on fractals, Indiana University Mathematics Journal 52 (2003), 133-156.

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[R91]" Function spaces on fractals, Journal of Functional Analysis 198 (2003), 43-83.

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[R92]" (with Richard Oberlin and Brian Street) Sampling on the Sierpinski gasket, Experimental Mathematics 12 (2003), 403-418.

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[R93]" Fractafolds based on the Sierpinski gasket and their spectra, Transactions American Mathematical Society 355 (2003), 4019-4043.

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[R94]" (with P. Edward Herman and Roberto Peirone) p-energy and p-harmonic functions on Sierpinski gasket type fractals, Potential Analysis 20 (2004), 125-148.

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[R95]" (with Carto Wong) The p-Laplacian on the Sierpinski gasket, Nonlinearity 17 (2004), 595-616.

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[R96*]" (with Robert Meyers and Alexander Teplyaev) Dirichlet forms on the Sierpinski gasket, Pacific Journal of Mathematics, to appear.

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[R97]" (with Jonathan Needleman, Alexander Teplyaev and Po-Lam Yung) Calculus on the Sierpinski gasket I: polynomials, exponentials and power series, Journal of Functional Analysis 215 (2004), 290-340.

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[R98*]" (with Kevin Coletta and Kealey Dias) Numerical analysis on the Sierpinski gasket, with applications to Schrödinger equation, wave equation and Gibbs' phenomenon, Fractals, to appear.

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[R99*]" Analysis on products of fractals, Transactions American Mathematical Society, to appear.

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[R100*]" Laplacians on fractals with spectral gaps have nicer Fourier series, submitted for publication.

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[R101*]" (with Kasso Okoudjou) Weak uncertainty principles on fractals, submitted for publication.

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[R102*]" (with Nitsan Ben-Gal, Abby Shaw-Krauss, and Clint Young) Calculus on the Sierpinski gasket II: point singularities, eigenfunctions, and normal derivatives of the heat kernel, submitted for publication.

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[R103*]" (with Shawn Drenning, Judith Palagallo and Thomas Price) Outer boundaries of self-similar tiles, submitted for publication.

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[E1]" Radon inversion - variations on a theme, American Mathematical Monthly, 89 (1982), 377-384, 420-423.

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[E2]" Para-differential operators - Another step forward for the method of Fourier, Notices of the American Mathematical Society, 29 (1982), 402-406.

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[E3]" Mathematics on display, Mathematical Intelligencer, 5 (1983), 37-40.

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[E4]" What's up, moonface?, UMAP Journal, 6 (1985), 3-34.

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[E5]" Realms of mathematics: elliptic, hyperbolic, sub-elliptic, Mathematical Intelligencer, 9 (1987), 56-64.

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[E6]" Book review of ``Noncommutative harmonic analysis'' by Michael E. Taylor, Bulletin of the American Mathematical Society, 17 (1987), 152-156.

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[E7]" (with R. R. Coifman, G. Graziosi and J. Hallquist) The School of Zygmund in ``A Century of Mathematics in America III'', American Mathematical Society (1989), 343-368.

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[E8]" Book review of ``Heat kernels and spectral theory'', by E. B. Davis, Bulletin (New Series) of the American Mathematical Society, 23 (1990), 222-227.

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[E9]" How to make wavelets, American Mathematical Monthly, 100 (1993), 539-556.

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[E10]" Construction of Orthonormal Wavelets. Wavelets: Mathematics and Applications, (J. Benedetto and M. Frazier, eds.) (1993), CRC Press.

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[E11]" Self-similarity in harmonic analysis (Survey article), Journal of Fourier Analysis and Applications, 1 (1994), 1-37.

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[E12]" Analysis on fractals, Notices American Mathematical Society 46 (1999), 1199-1208.

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[E13]" Evaluating integrals using self-similarity, American Mathematical Monthly, 107 (2000), 316-326.

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[U1]" The bouncing ball - an exercise in mathematical modeling

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[U2]" What to do till the topologist comes ( mathematical activities for children).

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[B1]" A guide to distribution theory and Fourier transforms, World Scientific Publishing, 2003 (reprinted from 1993 CRC Press edition).

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[B2]" The way of analysis, Jones and Bartlett Publishers, 1995.

(created by students working under my supervision)

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[W1]" Michael Gibbons and Arjun Raj, The finite element method on the Sierpinski gasket (1999), http://www.mathlab.cornell.edu/ ^~ gibbons

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[W2]" Nina (Tillman) Huang, Sampling theory for functions with fractal spectrum (2000), http://www.mathlab.cornell.edu/ ^~ tillman

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[W3]" Gregory Padowski, Harmonic mappings of the Sierpinski gasket (2000), http://www.mathlab.cornell.edu/ ^~ gp36

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[W4]" Scott Bailey and Theodore Kim, Lévy's dragon (2001),

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[W5]" P. Edward Herman, p-energy on the Sierpinski gasket (2001),

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[W6]" Richard Oberlin and Brian Street, Sampling on the Sierpinski gasket (2001), http://www.mathlab.cornell.edu/ ^~ brian/sampling/

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[W7]" Alex Smith, The finite element method on the pentagasket (2002),

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[W8]" Carto Wong, p-Laplacian on the Sierpinski gasket (2002),

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[W9]" Jonathan Needleman and Polam Yung, Polynomials and power series on the Sierpinski gasket (2002), http://www.mathlab.cornell.edu/ ^~ nman/

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[W10]" Kevin Coletta, The finite element method on the Sierpinski gasket (2002), http://www.mathlab.cornell.edu/ ^~ coletk/

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[W11]" Kealey Dias, Fourier series on fractals (2003),

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[W12]" Nitsan Ben-Gal, Normal derivatives and polynomials on the Sierpinski gasket (2003), www.math.cornell.edu/ ^~ bengal/

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[W13]" Abby Shaw-Krauss, Singularities at periodic points of the Sierpinski gasket (2003), www.math.cornell.edu/ ^~ abbysk/

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[W14]" Clint Young, Infinite blow-ups of the Sierpinski gasket (2003),

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[W15]" Brian Bockelman, Finite element method (2003),

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[W16]" Shawn Drenning, Self Similar Tiles (2004),

Index by Topics

Bounded mean oscillation: R26, R28

Cauchy transforms: R67

Elliptic partial differential equations: R14, R17, R25

Energy partition: R90

Experimental mathematics: R54, R61, R63, R64, R67, R69, R71, R73, R77, R81,

       R82, R83, R84, R85, R88, R89, R92, R94, R95, R97, R98, R102, R103, W1,

       W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15, W16

Finite element method: R78, R83, R89, R93, R98, W1, W7, W10, W15

Fourier transforms: R20, R23, R24, R31, R43, R44, R45, R46, R49, R54, R56, R64,

       R79, E11

Fourier series: R78, R79, R100

Fractafolds: R93

Fractal differential equations: R71, R74, R75, R76, R77, R81, R82, R83, R84, R86,

       R87, R89, R90, R91, R92, R93, R94, R95, R96, R97, R98, R99, R100, R101,

       R102, E12, W1, W3, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14,

       W15

Fractals and self-similarity: R46, R49, R51, R52, R53, R54, R55, R56, R57, R60,

       R61, R64, R65, R66, R67, R68, R69, R70, R71, R72, R73, R74, R75, R76,

       R77, R79, R81, R82, R83, R84, R85, R86, R87, R88, R89, R90, R91, R92,

       R93, R94, R95, R96, R97, R98, R99, R100, R101, R102, R103, E11, E12, E13,

       W1, W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12, W13, W14, W15,

       W16

Gibbs' phenomenon: R78, R98, W11

Green's functions: R81

Hardy spaces: R15, R17, R47

Harmonic analysis on symmetric spaces: R13, R18, R19, R20, R21, R23, R29, R30,

       R38, R42, R43, R44, R58, R59

Harmonic mappings: R86, W3

Heat semigroups: R35, R37, R51, R71, R102, W12

Heisenberg group: R44, R50, R53, R59, R62

Isoperimetric estimates: R70

Lévy dragon: R72, R88, R103, W4, W16

L^p estimates: R6, R7, R8, R9, R13, R17, R19, R29, R35, R37, R44, R50, R63, R91

Measures: R46, R49, R51, R52, R53, R54, R55, R56, R61, R64, R67, R68, R69,

       R79, R85, R87, E11, E13, W2

Nilpotent Lie groups: R12, R22, R44, R50, R53

p-Laplacian: R94, R95, W5, W8

Pseudodifferential operators: R12, R14, E2

Radon transforms: R29, R38, R50, R60, E1

Riemannian geometry: R35, R37, R41, R51

Sampling theory: R79, R85, R92, W2, W6

Singular integrals: R22, R32, R33

Sobolev spaces: R3, R4, R5, R11, R16, R26, R28, R34, R35, R47, R58, R65, R91,

       R99

Spectral theory of Laplacians: R35, R36, R44, R48, R51, R59, R62, R71, R74, R75,

       R83, R89, R93, R100, W7

Splines: R78, R82, R83, R98, W1, W7, W10, W15

Sub-Riemannian geometry: R39, R40, R53, E5

Taylor approximations: R76, R97, R102, W9, W12, W13

Tilings: R53, R57, R72, R73, R88, R103, W4, W16

Uncertainty principle: R43, R101

Wave equations: R8, R9, R10, R24, R25, R27, R30, R71, R98, W10

Wavelets: R52, R54, R57, R65, R80, E9, E10