**Contemporary Mathematics**

Volume: 251;
2000;
508 pp;
Softcover

Print ISBN: 978-0-8218-1148-1

Product Code: CONM/251

List Price: $110.00

Individual Member Price: $88.00

**Electronic ISBN: 978-0-8218-7841-5
Product Code: CONM/251.E**

List Price: $110.00

Individual Member Price: $88.00

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

Share this page *Edited by *
*E. L. Grinberg; S. Berhanu; M. Knopp; G. Mendoza; E. T. Quinto*

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

# Table of Contents

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

- Contents vii8 free
- Preface xi12 free
- On a problem of injectivity for the Radon transform on a paraboloid 114 free
- Anti-self-dual symplectic forms and integral geometry 1528
- Holomorphic extendibility of functions via nonlinear Fourier transforms 2740
- Division-interpolation methods and Nullstellensätze 4154
- Uniqueness and non-uniqueness for microanalytic continuation of ultradistributions 6174
- A rational Landen transformation. The case of degree six 8396
- A perturbation result for linear differential operators admitting a global right inverse on D' 93106
- Weyl's law with error estimate 107120
- Dirac equation in the octonionic algebra 117130
- A note on Siegel's proof of Hamburger's theorem 135148
- Sheaves and D-modules in integral geometry 141154
- Positivity conditions and squared norms of holomorphic polynomial mappings 163176
- The exponential X-ray transform and Fritz John's equation. I. Range description 173186
- Two lemmas in local analytic geometry 189202
- Partitions and theta constant identities 197210
- The Radon transform and spectral rigidity of the Grassmannians 205218
- Complex powers of convolution operators on the Heisenberg group 223236
- Estimates for generalized Radon transforms in three and four dimensions 243256
- Irregular sampling and the Radon transform 255268
- Involution of Λ-adic analytic spaces and the Up-operator for half-integral weight modular forms 269282
- Maximal sequences of compact Riemann surfaces 277290
- On BMO singularities of solutions of analytic complex vector fields 295308
- The initial value problem for a fifth order shallow water equation on the real line 309322
- Mappings between degenerate real analytic hypersurfaces in Cn 321334
- Analysis of artifacts in local tomography with nonsmooth attenuation 339352
- The Hecke convergence factor and modular forms of weight zero 371384
- Hypoellipticity at points of infinite type 393406
- Semi-global analytic regularity for ∂b on CR submanifolds of C2 399412
- Cauchy transform and Hardy spaces for rough planar domains 409422
- On real analytic planar vector fields near the character set 429442
- On longest increasing subsequences in random permutations 439452
- Convergence of Poincaré series with two complex coweights 453466
- Eisenstein series and Eichler integrals 463476
- Real hypersurfaces with no infinitesimal CR automorphisms 469482
- Extension of cohomology classes 475488
- Two-radius support theorems for spherical Radon transforms on manifolds 501514

#### Readership

Graduate students and research mathematicians; industrial and applied mathematicians.