**Contemporary Mathematics**

Volume: 137;
1992;
478 pp;
Softcover

MSC: Primary 30; 32;
Secondary 42; 47

Print ISBN: 978-0-8218-5147-0

Product Code: CONM/137

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

**Electronic ISBN: 978-0-8218-7728-9
Product Code: CONM/137.E**

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

# The Madison Symposium on Complex Analysis

Share this page *Edited by *
*Edgar L Stout; Alexander J. Nagel*

This volume contains the proceedings of a Symposium on Complex Analysis, held at the University of Wisconsin at Madison in June 1991 on the occasion of the retirement of Walter Rudin. During the week of the conference, a group of about 200 mathematicians from many nations gathered to discuss recent developments in complex analysis and to celebrate Rudin's long and productive career. Among the main subjects covered are applications of complex analysis to operator theory, polynomial convexity, holomorphic mappings, boundary behavior of holomorphic functions, function theory on the unit disk and ball, and some aspects of the theory of partial differential equations related to complex analysis. Containing papers by some of the world's leading experts in these subjects, this book reports on current directions in complex analysis and presents an excellent mixture of the analytic and geometric aspects of the theory.

#### Readership

Advanced graduate students and researchers in complex analysis and related subjects.

#### Reviews & Endorsements

Among the authors are some of the world's leading experts. Therefore this volume is an excellent report on current directions in complex analysis. It is a tribute to Walter Rudin in so far as much of the work contained in this book makes contact with work that he has done over the last forty years.

-- Monatshefte für Mathematik

# Table of Contents

## The Madison Symposium on Complex Analysis

- Contents v6 free
- Preface ix10 free
- Hulls of 3-spheres in C3 112 free
- On the totally real spheres of Ahern and Rudin and Weinstein 2940
- Dominant sets on the unit sphere of Cn 3748
- The Cauchy transform, the Szegö projection, the Dirichlet problem, and the Ahlfors map 4354
- Variations on the theorem of Morera 6374
- A remark on local continuous extension of proper holomorphic mappings 7990
- A multivariable version of the Müntz-Szasz theorem 8596
- On A∞ interpolating sets lying on curves 93104
- Vanishing cup products on pseudoconvex CR manifolds 105116
- Ext for Hilbert modules 113124
- Hardy spaces and elliptic boundary value problems 119130
- Représentation intégral de certaines classes de jets de Whitney 133144
- A class of hypoelliptic PDE admitting non-analytic solutions 155166
- Fourier analysis off groups 169180
- Uniform extendibility of automorphisms 177188
- The class L log L with weights 185196
- The geometry of proper holomorphic maps between balls 191202
- Contractive zero-divisors in Bergman spaces 217228
- The theorem of F. and M. Riesz for unbounded measures 221232
- Intersections of analytic and smooth discs 235246
- Critically finite rational maps on P2 245256
- A disc in the ball approaching the boundary non-nontangentially 261272
- On hypoellipticity for sums of squares of vector fields 267278
- Composition operators in Bergman spaces on bounded symmetric domains 277288
- Isotopic embeddings of affine algebraic varieties into Cn 291302
- Polynomial solutions of the Fueter-Hurwitz equation 297308
- Corona problem of several complex variables 307318
- Sharp estimates of the Kobayashi metric near strongly pseudoconvex points 329340
- Proper maps, complex geodesics and iterates of holomorphic maps of convex domains in Cn 339350
- On the polynomial hull of two balls 343354
- Analytic automorphisms of C2 which preserve the coordinate axes 351362
- Analytic transversality and nullstellensatz in Bergman space 367378
- On the radial maximal function and the Hardy Littlewood maximal function in wedges 383394
- Local and semi-global existence theorems for ∂b on C R manifolds 399410
- Making an outer function from two inner functions 407418
- Arclength formulas in conformal mapping 415426
- Sharp geometric estimates of the distance to VMOA 421432
- On the one-dimensional extension property 433444
- Analytic Г-almost-periodic structures in algebra spectra 445456
- Recurrence for lacunary cosine series 459470
- Maximum modulus algebras 469480