Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis

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.

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