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Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis
Edited by: E. L. Grinberg, S. Berhanu, M. Knopp, and G. Mendoza, Temple University, Philadelphia, PA, and E. T. Quinto, Tufts University, Medford, MA

Contemporary Mathematics
2000; 508 pp; softcover
Volume: 251
ISBN-10: 0-8218-1148-7
ISBN-13: 978-0-8218-1148-1
List Price: US$110
Member Price: US$88
Order Code: CONM/251
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This book presents the proceedings from a conference at Temple University celebrating the work of Leon Ehrenpreis, distinguished by its insistence upon getting to the heart of the mathematics and by its astonishing consistency in doing so successfully. Professor Ehrenpreis has worked in many areas of mathematics and has found connections among all of them. For example, we can find his analysis ideas in the context of number theory, geometric thinking within analysis, transcendental number theory tied to partial differential equations. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work.

The collection of articles presents current research on PDE's, several complex variables, analytic number theory, integral geometry and tomography. The thinking of Professor Ehrenpreis has contributed fundamental concepts and techniques in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.


Graduate students and research mathematicians; industrial and applied mathematicians.

Table of Contents

  • M. Agranovsky -- On a problem of injectivity for the Radon transform on a paraboloid
  • J. C. Álvarez -- Anti-self-dual symplectic forms and integral geometry
  • T. T. Banh -- Holomorphic extendibility of functions via nonlinear Fourier transforms
  • C. A. Berenstein and A. Yger -- Division-interpolation methods and Nullstellensätze
  • J. Boman -- Uniqueness and non-uniqueness for microanalytic continuation of ultradistributions
  • G. Boros and V. H. Moll -- A rational Landen transformation. The case of degree six
  • R. W. Braun, R. Meise, and B. A. Taylor -- A perturbation result for linear differential operators admitting a global right inverse on \(\mathcal{D}^\prime\)
  • S. Catto, J. Huntley, N. Moh, and D. Tepper -- Weyl's law with error estimate
  • F. Colombo, I. Sabadini, and D. C. Struppa -- Dirac equation in the octonionic algebra
  • W. Culp-Ressler and W. d. A. Pribitkin -- A note on Siegel's proof of Hamburger's theorem
  • A. D'Agnolo -- Sheaves and \(\mathcal{D}\)-modules in integral geometry
  • J. P. D'Angelo -- Positivity conditions and squared norms of holomorphic polynomial mappings
  • L. Ehrenpreis, P. Kuchment, and A. Panchenko -- The exponential x-ray transform and Fritz John's equation. I. Range description
  • C. L. Epstein and G. M. Henkin -- Two lemmas in local analytic geometry
  • H. M. Farkas and I. Kra -- Partitions and theta constant identities
  • J. Gasqui and H. Goldschmidt -- The Radon transform and spectral rigidity of the Grassmannians
  • D. Geller -- Complex powers of convolution operators on the Heisenberg group
  • A. Greenleaf, A. Seeger, and S. Wainger -- Estimates for generalized Radon transforms in three and four dimensions
  • E. Grinberg and I. Pesenson -- Irregular sampling and the Radon transform
  • P. Guerzhoy -- Involution of \(\Lambda\)-adic analytic spaces and the \(U_p\)-operator for half-integral weight modular forms
  • R. C. Gunning -- Maximal sequences of compact Riemann surfaces
  • J. Hounie and J. Tavares -- On BMO singularities of solutions of analytic complex vector fields
  • A. A. Himonas and G. Misiołek -- The initial value problem for a fifth order shallow water equation on the real line
  • X. Huang, J. Merker, and F. Meylan -- Mappings between degenerate real analytic hypersurfaces in \(C^n\)
  • A. Katsevich -- Analysis of artifacts in local tomography with nonsmooth attenuation
  • M. I. Knopp and W. d. A. Pribitkin -- The Hecke convergence factor and modular forms of weight zero
  • J. J. Kohn -- Hypoellipticity at points of infinite type
  • M. Derridj and D. S. Tartakoff -- Semi-global analytic regularity for \({{\overline{\partial}}_b}\) on CR submanifolds of \(\mathbb{C}^2\)
  • L. Lanzani -- Cauchy transform and Hardy spaces for rough planar domains
  • A. Meziani -- On real analytic planar vector fields near the character set
  • A. M. Odlyzko and E. M. Rains -- On longest increasing subsequences in random permutations
  • P. C. Pasles -- Convergence of Poincaré series with two complex coweights
  • W. d. A. Pribitkin -- Eisenstein series and Eichler integrals
  • N. K. Stanton -- Real hypersurfaces with no infinitesimal CR automorphisms
  • F. Treves -- Extension of cohomology classes
  • Y. Zhou and E. T. Quinto -- Two-radius support theorems for spherical Radon transforms on manifolds
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