CONTEMPORARY MATHEMATICS 455 Israel Mathematical Conference Proceedings Complex Analysis and Dynamical Systems Ill A Conference in Honor of the Retirement of Dov Aharonov, Lev Aizenberg, Samuel Krushkal, and Uri Srebro January 2-6, 2006 Nahariya, Israel Mark Agranovsky Daoud Bshouty Lavi Karp Simeon Reich David Shoikhet Lawrence Zalcman http://dx.doi.org/10.1090/conm/455

Complex Analysis and Dynamical Systems Ill Titles in This Subseries

Israel Mathematical Conference Proceedings (IMCP) is a publication, part of the Contemporary Mathematics Series, devoted to the proceedings of conferences, symposia and seminars. Collections of papers focusing on a certain subject will also be published. Prospective volumes may be submitted to any member of the editorial board. Each volume has an editor (or editors) responsible for its preparation. In order to ensure inexpensive and timely distribution, authors are requested to submit to the Editor of the volume an electronic 'lEX file of their manuscript in A_MS-~'IEX. using the Contemporary Mathematics style file which can be downloaded at http://www.ams.org/tex/author-info.html. For further information, contact the Managing Editor, IMCP, Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel; e-mail: roweniDmacs. biu. ac. il. 455 Mark Agranovsky, Daoud Bshouty, Lavi Karp, Simeon Reich, David Shoikhet, and Lawrence Zalcman, Editors, Complex Analysis and Dynamical Systems III, 2008 433 Pavel Etingof, Shlomo Gelaki, and Steven Shnider, Editors, Quantum groups, 2007 404 Alexander Borichev, Hakan Hedenmalm, and Kehe Zhu, Editors, Bergman spaces and related topics in complex analysis, 2006 402 Zvi Arad, Mariagrazia Bianchi, Wolfgang Herfort, Patrizia Longobardi, Mercede Maj, and Carlo Scoppola, Editors, Ischia group theory 2004, 2006 387 Michael Entov, Yehuda Pinchover, and Michah Sageev, Editors, Geometry, spectral theory, groups, and dynamics, 2005 382 Mark Agranovsky, Lavi Karp, and David Shoikhet, Editors, Complex analysis and dynamical systems II, 2005 364 Mark Agranovsky, Lavi Karp, David Shoikhet, and Lawrence Zalcman, Editors, Complex analysis and dynamical systems, 2004

Published Earlier as IMCP 15 Vitali Milman, Iossif Ostrovskii, Mikhail Sodin, Vadim Tkachenko, and Lawrence Zalcman, Editors, Entire functions in modern analysis: Boris Levin memorial conference, 2001 14 Robert Brooks and Mikhail Sodin, Editors, Lectures in memory of Lars Ahlfors, 2000 13 Yuri Brudnyi, Michael Cwikel, and Yoram Sagher, Editors, Function spaces, interpolation spaces, and related topics, 1999 12 Mina Teicher, Editor, The heritage of Emmy Noether, 1999 11 Lawrence Zalcman, Editor, Proceedings of the Ashkelon workshop on complex function theory (May 1996), 1997 10 Jean-Pierre Fouque, Kenneth J. Hochberg, and Ely Merzbach, Editors, Stochastic analysis: random fields and measure-valued processes, 1995 9 Mina Teicher, Editor, Proceedings of the Hirzebruch 65 conference on algebraic geometry, 1995 8 Ilya Piatetski-Shapiro and Stephen Gelbart, Editors, The Schur lectures (1992), 1995 7 Anthony Joseph and Steven Shnider, Editors, Quantum deformations of algebras and their representations, 1993 6 Haim Judah, Editor, Set theory of the reals, 1992 5 Michael Cwikel, Mario Milman, and Richard Rochberg, Editors, Interpolation spaces and related topics, 1992 4 Simson Baron and Dany Leviatan, Editors, Approximation interpolation and summability, in honor of Amnon Jakimovski, 1991 3 Stephen Gelbart, Roger Howe, and Peter Sarnak, Editors, Festschrift in honor of I. I. Piatetski-Shapiro, part II: Papers in analysis, number theory and automorphic £-Functions, 1990 (Continued in the back of this publication) CoNTEMPORARY MATHEMATICS

455

Israel Mathematical Conference Proceedings

Complex Analysis and Dynamical Systems Ill

A Conference in Honor of the Retirement of Dov Aharonov, Lev Aizenberg, Samuel Krushkal, and Uri Srebro January 2-6, 2006 Nahariya, Israel

Mark Agranovsky Daoud Bshouty Lavi Karp Simeon Reich David Shoikhet Lawrence Zalcman

American Mathematical Society Providence, Rhode Island

Bar-llan University Ramat Gam, Israel Editorial Board of Contemporary Mathematics Dennis DeTurck, managing editor George Andrews Andreas Blass Abel Klein

Editorial Board of Israel Mathematical Conference Proceedings Louis Rowen, Bar-Ilan University, managing editor Z. Arad, Netanya Academic College M. Katz, Bar-Ilan University J. Bernstein, Tel-Aviv University B. Pinchuk, Netanya Academic College H. Furstenberg, Hebrew University S. Shnider, Bar-Ilan University S. Gelbart, Weizmann Institute L. Small, University of California at San Diego V. Gol'dshtein, Ben-Gurion University L. Zalcman, Bar-Ilan University Miriam Beller, Technical Editor

2000 Mathematics Subject Classification. Primary 74-xx, 30-xx, 31-xx, 32-xx, 35-xx, 37-xx, 41-xx, 42-xx, 46-xx, 47-xx, 53-xx, 57-xx.

Library of Congress Cataloging-in-Publication Data International Conference on Complex Analysis and Dynamical Systems (3rd : 2006 : Nahariya, Israel) Complex analysis and dynamical systems III : a conference in honor of the retirement of Professors Dov Aharonov, Lev Aizenberg, Samuel Krushkal, and Uri Srebro, January 2--6, 2006, Nahariya, Israel/ Mark Agranovsky .... [eta!.]. p. cm.-(Israel mathematical conference proceedings) Contemporary mathematics, ISSN 0271-4132); v. 455) Includes bibliographical references. ISBN 978-0-8218-4150-1 (alk. paper) 1. Functions of complex variables-Congresses. 2. Differentiable dynamical systems-Con- gresses. QA331.7.158 2006 515.9-dc22 2008060011

Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Managing Editor, IMCP, Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900 Israel. Requests can also be made by email to rowen\Omacs. biu. ac. il. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) © 2008 by Bar-Ilan University. Printed in the United States of America. i§l The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http: I /www. ams. org/ 10 9 8 7 6 5 4 3 2 1 13 12 11 10 09 08 Contents

Preface ix Biographies xi Conference Program xiii List of participants xxi Stable Expansions in Homogeneous Polynomials L. AIZENBERG and N. TARKHANOV 1 Dynamics of Approximate Solutions to a Class of Evolution Equations in Banach Spaces S. AIZICOVICI, S. REICH, and A.J. ZASLAVSKI 23 Schottky's Theorem on Conformal Mappings Between Annuli K. ASTALA, T. lWANIEC, G. MARTIN, and J. ONNINEN 35 Univalent Convex Functions in the Positive Direction of the Real Axis D. BSHOUTY and A. LYZZAIK 41 The Common Fixed Point Set of Commuting Nonexpansive Mappings in Infinite Products of Unit Balls M. BUDZYNSKA and T. KUCZUMOW 53 Controlled Approximation for Some Classes of Holomorphic Functions M. ELIN, D. SHOIKHET, and L. ZALCMAN 63

Best Approximating Entire Functions to lxla in £ 2 M.l. GANZBURG and D.S. LUBINSKY 93 Orbits of Tori Extended by Finite Groups and their Polynomial Hulls: The Case of Connected Complex Orbits V.M. GICHEV 109 QC Riemann Mapping Theorem in Space D.H. HAMILTON 131 Boundary Value Problems in Weighted Edge Spaces G. HARUTYUNYAN and B.-W. SCHULZE 151 Analytic Properties of Besov Spaces via Bergman Projections H.T. KAPTANOGLU and A. ERSiN UREYEN 169 The Cauchy integral over non-rectifiable paths B.A. KATS 183

v vi CONTENTS

Holomorphic Continuation via Laplace-Fourier series 0. KOUNCHEV and H. RENDER 197 Analytic Functions in Algebras Y. KRASNOV 207 Rational Approximation of Holomorphic Functions and Geometry of Grunsky Inequalities S.L. KRUSHKAL 219 Quadratic Forms in Geometric Function Theory, Quasiconformal Extensions, Fredholm Eigenvalues R. KUHNAU 237 Elimination Methods of Unknowns from Nonlinear Systems A. KYTMANOV 257 On Locally Biholomorphic Finitely Valent Mappings from Multiply Connected to Simply Connected Domains P. LICZBERSKI and V.V. STARKOV 269 Parabolic Pseudodifferential Operators in Exponential Weighted Spaces YA. LUTSKY and V.S. RABINOVICH 279 The Cauchy Problem of Couple-Stress Elasticity 0. MAKHMUDOV, I. NIYOZOV, and N. TARKHANOV 297 On the Zeta-function of a Nonlinear System S. MYSLIVETS 311 Some Questions of Uniqueness for Extremal Quasiconformal Mappings E. REICH 317 Remarks on the Existence of Quasimeromorphic Mappings E. SAUCAN 325 On the Cauchy Problem for the Cauchy-Riemann Operator in Sobolev Spaces A. SHLAPUNOV 333 On Spectral Functions for Commutative J-self-adjoint Operator Families of the D-:_ -class V. STRAUSS 349 Mappings Associated with Weighted Sobolev Spaces A. UKHLOV and S.K. VoDOPYANOV 369 Inner Maps and Banach Algebras E. VESENTINI 383 Reconstructing Holomorphic Functions in a Domain from their Values on a Part of its Boundary A. VIDRAS 393 A Note on the Parabolicity of Minimal Graphs A. WEITSMAN 411 CONTENTS vii

Localization of Fixed Points and Zeros for Holomorphic Maps in Locally Convex Spaces and Nonexpansive Maps in J*-algebras K. WLODARCZYK, D. KLIM, and R. KowALCZYK 417 On Harmonic Polynomial Interpolation V. ZAHARIUTA 439 Preface

The Third International Conference on Complex Analysis and Dynamical Systems ( CA&DS III), sponsored by ORT Braude College {Karmiel, Israel), Bar-Ilan University, and the Technion, took place at the Carlton Hotel in Nahariya, Israel, during January 2-6, 2006. This was the seventh in a series of mathemat- ics conferences organized by ORT Braude over the past several years. Altogether, over 100 participants from 20 countries attended the Conference, which was held in honor of Professors Dov Aharonov, Lev Aizenberg, Samuel Krushkal, and Uri Srebro, on the occasion of their retirement. This volume is the tangible record of CA&DS III. Most of the papers collected here have been contributed by participants in the Conference. In some cases, they have chosen to submit manuscripts which depart from the texts of their lectures. There are also contributions from participants who did not speak at the Conference, as well as papers by friends and admirers of the honorees who were unable to attend. All submissions have been carefully refereed. We acknowledge with thanks the support provided for the Conference by the Galilee Research Center for Applied Mathematics of ORT Braude, the Gelbart Research Institute for Mathematical Sciences and the Emmy Noether Research Institute for Mathematics of Bar-Ilan University and the Center of Mathematical Sciences (under the auspices of the Elisha Netanyahu Institute of Advanced Studies in Mathematics). Special thanks to the technical editor, Miriam Beller, for work above and beyond the call of duty and to Larry Zalcman, who (as in previous volumes) has edited the papers for English style.

The Editors

ix Biographies

Professor Dov Aharonov was born in Haifa in 1938 and received his D.Sc from the Technion-ITT in 1967, under the guidance of Elisha Netanyahu. After postdoctoral studies at the University of Maryland, he joined the Department of Mathematics at the Technion. His research ranges over complex analysis as a whole, including geometric function theory, ordinary differential equations, quadrature domains, dynamical systems and circle packings. Prof. Aharonov has written three monographs and published over fifty research papers. Many of the Israeli mathematicians working in his fields of interest have been his students.

Professor Lev Aizenberg was born in Moscow in 1937. He graduated from the Moscow Pedagogical Insitute in 1961 with a Ph.D. in mathematics under the guidance of A. Temliakov {who was a student of S. Berman) and received his D.Sc. in 1967 from Moscow State University. In 1964, at the General Physics Institute of the Siberian Branch of the Russian Academy of Science in Krasnoyarsk, he founded the Laboratory of Function Theory. At the same time, he founded the Department of Mathematical Analysis at the University of Krasnoyarsk. In 1993, he immigrated to Israel. Since 1994, he has served as a professor in the Department of Mathematics, Bar-Ilan University. Prof. Aizenberg has published over 140 research papers, including three monographs. He has had 25 Ph.D. students, eight of whom are full professors.

Professor Samuel L. Krushkal was born in Tartu, Estonia in 1938 and grad- uated from the Sobolev Institute of Mathematics with a Ph.D. in 1964 and with a D.Sc. in mathematics in 1970 under the guidance of P. Belinskii. He was a research scientist at the Sobolev Institute until 1991, when he joined the Department of Mathematics at Bar-Ilan University. His research interests include complex analy- sis, geometric function theory, differential geometry, differential equations, and the geometry and topology of manifolds. He is the author and editor of four books and has published over 120 research papers. He has had 21 Ph.D. students from all over the world.

Professor Uri Srebro was born in Tel Aviv in 1936 and received his D.Sc. from the Technion- ITT in 1968, with Elisha Netanyahu as his thesis advisor. After postdoctoral studies at the University of Minnesota and shorter visits to Urbana and Helsinki, he returned to the Technion in 1969 and has been there ever since. His areas of research and interest include quasiconformal and quasiregular mappings, Beltrami equations, branched folded mappings, covering theorems for meromorphic functions, immersions of manifolds and discrete Moebius groups. He was one of the organizers of the Special Year in Complex Analysis at the Technion in 1975-76 and

xi xii BIOGRAPHIES later very active in organizing international conferences in his fields of interest. He has also been a long-term visitor at many of the leading centers of complex analysis, including Maryland, Helsinki, Jyvaskyla, Ann Arbor, San Diego, Purdue, Uppsala, New Zealand and Urbana-Champaign. Conference Program

January 2-6, 2006

Monday, January 2 08:30 Registration at Carlton Hotel 14:00-14:15 Opening Ceremony Plenary Talks 14:20 - 15:05 0. Martio On the regularity of quasiconformal maps with applications

15:10- 15:55 N. Tarkhanov Analytic continuation from a boundary subset

Afternoon Session 1 16:30 - 17:00 S. Ruscheweyh Circular convexity preservation under Hadamard products

17:05 - 17:35 M. Stawiska Currents and the topology of invariant sets for holomorphic maps in several variables

17:40 - 18:10 0. Roth A boundary version of Ahlfors' Lemma with applications

18:15 - 18:45 E. Liflyand Hausdorff operators on the real Hardy space

18:50-19:20 V. Zahariuta Some applications of pluripotential theory in complex analysis

xiii xiv CONFERENCE PROGRAM

Afternoon Session 2 16:30 - 17:00 W. Abikoff Computations and generalizations of the Douady-Earle extension

17:05 - 17:35 A. Weitsman Parabolicity criteria for minimal surfaces with boundary

17:40- 18:10 K. Dyakonov Self-improving behavior of inner functions as multipliers

18:15- 18:45 W. Littman Boundary control "lite" Afternoon Session 3 16:30- 17:00 S. Friedland Entropy of holomorphic and rational maps

17:05 - 17:35 I. Sarantopoulos Generalization of Hardy-Hilbert inequality

17:40 - 18:10 V. Strauss On the bicommutant of a commutative W J* -algebra of D"!; -class

18:15- 18:45 T. Kuczumow Properties of the Kobayashi distance and fixed points of holomorphic mappings

18:50-19:20 L. Rodman Analytic roots of invertible matrix functions

Tuesday, January 3 Plenary Talks 08:30- 09:15 H.S. Shapiro Stefan Bergman's doubly orthogonal functions

09:20 - 10:05 M. Kapovich Critical exponent and cohomological dimension CONFERENCE PROGRAM XV

Morning Session 1 10:40- 11:10 D. Khavinson Algebraicity in the classical Dirichlet problem

11:15- 11:45 H. Render Real Bargmann spaces, Fischer pairs and sets of uniqueness for polyharmonic functions

11:50 - 12:20 A. Vidras Analytic functions representable by Carleman formulas

12:25 - 12:55 A. Shlapunov The Cauchy problem for the Cauchy Riemann system and mixed problem with a parameter Morning Session 2 10:40- 11:10 L. Potyagailo Right-angled Coxeter groups in the hyperbolic spaces

11:15 - 11:45 S. Krushkal Rational approximation of holomorphic functions and geometry of Grunsky inequalities

11:50 - 12:20 E. Saucan The existence of quasimeromorphic mappings

12:25 - 12:55 A. Golberg Differential properties of homeomorphisms with finite integral dilatations Morning Session 3 10:40- 11:10 B.-W. Schulze Edge calculus of second generation

11:15 - 11:45 E. Titi On the question of global regularity for the three- dimensional Navier-Stokes equations

11:50- 12:20 Y. Kametaka The best constant in Sobolev's inequality

12:25 - 12:55 V. Rabinovich Essential spectrum of discrete Schrodinger and Dirac operators and exponential estimates of their eigenfunctions

Plenary Talk 14:20- 15:15 D. Hamilton QC Riemann mapping theorem in space xvi CONFERENCE PROGRAM

Afternoon Session 1 15:35 - 16:05 M. Shapiro On polynomials, Taylor series and rational functions in Clifford analysis

16:10 - 16:40 P. Liczberski On locally biholomorphic mappings from multiply connected domains onto canonical domains

16:45- 17:15 Y. Krasnov Analytic functions in algebras

17:20 - 17:50 Y. Feler Spaces of geometrically generic configurations

Afternoon Session 2 15:35- 16:05 T. Kaptanoglu Bergman projections on Besov spaces on balls

16:10 - 16:40 V. Gutlyanskii On boundary regularity of conformal maps

16:45- 17:15 M.M. Lavrentiev Mathematical problems in tomography and hyperbolic reflections

17:20 - 17:50 E. Yakubov Ring homeomorphisms and the Beltrami equation

Afternoon Session 3 15:35- 16:05 K.Takemura A bending problem of a bar and the best constant in Sobolev's inequality

16:10 - 16:40 B. Paneah Another approach to the Ulam stability of linear functional equations

16:45- 17:15 L. Zelenko Generic spectrum of a Schrodinger operator with complex limit-periodic potential

17:20 - 17:50 A.M. Il'in The coefficients of inner asymptotic expansions for solutions of some singular boundary value problems CONFERENCE PROGRAM xvii

Wednesday, January 4

Plenary Talks

08:30 - 09:15 L. Zalcman Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros

09:20 - 10:05 E. Reich Recent progress and open questions for extremal quasiconformal mappings Morning Session 1 10:40- 11:10 J.M. Anderson A generalized Schwarz Pick Lemma

11:15- 11:45 L. Aizenberg Classical results of Bohr and Rogosinski on power series and their multivariate analogues

11:50 - 12:20 0. Kounchev Solution of the multivariate moment problem, or polyharmonic quadrature domains and Gauss Jacobi cubatures

12:25 - 12:55 L. Znamenskaya Martineau-Aizenberg duality in Kiselman's problem Morning Session 2

10:40- 11:10 I. Kra Some analytic aspects of Teichmiiller theory

11:50 - 12:20 H. Hedenmalm A refinement of Makarov's LIL

12:25 - 12:55 H.M. Farkas Theta function identities xviii CONFERENCE PROGRAM

Morning Session 3 10:40- 11:10 V. Derkach Convergence of Pade approximants for generalized Nevanlinna functions

11:15 - 11:45 D. Klim Fixed points of set-valued dynamical systems of upper semicontinuous asymptotic contractions

11:50 - 12:20 M. Ostrovskii Linear fractional relations: non-triviality of the domain and analogues of the Liouville theorem

12:25 - 12:55 I. Gaissinski Kelvin Helmholtz instability model for supersonic viscid jets

Afternoon Session 1 14:00 - 14:30 S. Myslivets On the zeta-function of a nonlinear system

14:35 - 15:05 B.A. Kats The Cauchy integral over non-rectifiable paths Afternoon Session 2 14:00 - 14:30 A. Eremenko Polya 's conjecture on the zeros of successive derivatives of real entire functions

14:35 - 15:05 A. Ukhlov Sobolev spaces and mappings with bounded mean distortion Afternoon Session 3 14:00- 14:30 A. Sidi A new approach to vector-valued rational interpolation

14:35 - 15:05 P. Yuditskii The renormalization of periodic Jacobi matrices and limit periodic matrices with a singular continuous spectrum

Thursday, January 5

Plenary Talks 08:30- 09:15 W.K. Hayman The growth of univalent functions with an initial gap

09:20 - 10:05 E. Vesentini Inner maps into Banach algebras CONFERENCE PROGRAM xix

Morning Session 1 10:40- 11:10 D. Lubinsky Best approximating entire functions of exponential type

11:15- 11:45 C. Beneteau A survey of extremal problems for non-vanishing analytic functions

Morning Session 2 11:15 - 11:45 L. Resendis Dirichlet Dp spaces

Morning Session 3 10:40- 11:10 K. Wlodarczyk Localization of fixed points and zeros of holomorphic maps in locally convex spaces and nonexpansive J* -algebras Friday, January 6 Plenary Talks 09:00 - 09:45 K. Stephenson Discrete conformal structure

09:50 - 10:35 R. Kiihnau Quadratic forms in geometric function theory

11:10- 11:55 A. Kytmanov Elimination methods of unknowns from nonlinear systems List of Participants

W. Abikoff Y. Feler University of Connecticut, USA The Technion, Israel B. Abramovich S. Friedland ORT Braude College, Israel University of Illinois at Chicago, USA M. Agranovsky I. Gaissinski Bar-Ilan University, Israel The Technion, Israel D. Aharonov A. Golberg The Technion, Israel Bar-Ilan University, Israel L. Aizenberg A. Gol'dberg Bar-Ilan University, Israel Bar-Ilan University, Israel J. M. Anderson A. Goldvard University College London, UK ORT Braude College, Israel A. Aytuna V. Gutlyanskii Sabanci Universitesi, Thrkey Institute of Applied Mathematics & Mechanics, NAS, Ukraine C. Beneteau Seton Hall University, USA D. Hamilton University of Maryland, USA D. Bshouty The Technion, Israel L. Hanin Idaho State University, USA M. Budzynska Maria Curie-Sklodowska University, W. K. Hayman Poland Imperial College, England V. Derkach H. Hedenmalm Donetsk National University, Ukraine Royal Institute of Technology, Sweden K. Dyakonov R. Hurri-Syrjanen Universitat de Barcelona, Spain University of Helsinki, Finland M. Elin A. Il'in ORT Braude College, Israel Chelyabinsk State University, Russia A. Eremenko F. Jakobzon Purdue University, USA ORT Braude College, Israel H. Farkas Y. Kametaka Hebrew University, Israel Osaka University, Japan

xxi xxii PARTICIPANTS

M. Kapovich M. Levenstein University of California Davis, USA The Technion, Israel T. Kaptanoglu E. Levin Bilkent University, Turkey The Open University, Israel

I. Karelin G. Levin ORT Braude College, Israel Hebrew University, Israel M. Karmanova P. Liczberski Novosibirsk State University, Russia Technical University of L6dz, Poland L. Karp E. Liflyand ORT Braude College, Israel Bar-Ilan University, Israel B. Kats W. Littman Kazan State University, Russia University of Minnesota, USA V. Khatskevich D. Lubinsky ORT Braude College, Israel Georgia Institute of Technology, USA D. Khavinson Y. Lutsky University of Arkansas, USA ORT Braude College, Israel D. Klim 0. Martio University of L6dz, Poland Universitas Helsingiensis, Finland 0. Kounchev R. Miniowitz Institute of Mathematics and The Technion, Israel Informatics, Bulgarian Academy of S. Myslivets Sciences, Bulgaria Krasnoyarsk State University, Russia I. Kra S. Nevo State University of New York at Stony Bar-Ilan University, Israel Brook, USA M. Ostrovskii Y. Krasnov St. John's University, USA Bar-Ilan University, Israel V. Palamodov S. Krushkal Tel-Aviv University, Israel Bar-Ilan University, Israel X. Pang T. Kuczumow East China Normal University, China Maria Curie-Sklodowska University, Poland B. Paneah The Technion, Israel R. Kiihnau Martin-Luther Universitiit, Germany L. Potyagailo Universite de Lille 1, France A. Kytmanov Siberian Federal University, Russia V. Rabinovich Instituto Politecnico Nacional, Mexico M. Lavrentiev Sobolev Institute of Mathematics, SB E. Reich RAS, Russia University of Minnesota, USA PARTICIPANTS xxiii

S. Reich V. Strauss The Technion, Israel Universidad Simon Bolivar, Venezuela H. Render K. Takemura Universidad de La Rioja, Spain Tokyo University of Technology, Japan L. Resendis N. Tarkhanov Metropolitan Autonomous University, Universitiit Potsdam, Germany Mexico M. Teicher L. Rodman Bar-Ilan University, Israel The College of William & Mary, USA E. Titi J. Roseman University of California, Irvine, USA Tel-Aviv University, Israel and The Weizmann Institute of Science, Israel 0. Roth Universitiit Wiirzburg, Germany A. Ukhlov Ben-Gurion University of the Negev, V. Rovenski Israel University of Haifa, Israel E. Vesentini S. Ruscheweyh Accademia Nazionale dei Lincei, Italy Universitiit Wiirzburg, Germany A. Vidras I. Sarantopoulos University of Cyprus, Cyprus National Technical University, Greece Y. Weit E. Saucan University of Haifa, Israel The Technion, Israel A. Weitsman B. W. Schulze Purdue University, USA Universitiit Potsdam, Germany K. Wlodarczyk H. Shapiro University of L6dz, Poland Kungliga Tekniska Hogskolan, Sweden E. Yakubov M. Shapiro Holon Academic Institute of Instituto Politecnico N acional, Mexico Technology, Israel T. Sheil-Small P. Yuditskii University of York, England Bar-Ilan University, Israel A. Shlapunov V. Zaharyuta Siberian Federal University., Russia Sabanci Universitesi, Turkey D. Shoikhet L. Zalcman ORT Braude College, Israel Bar-Ilan University, Israel L. Shvartsman L. Zelenko ORT Braude College, Israel University of Haifa, Israel U. Srebro L. Znamenskaya The Technion, Israel Program Systems Institute, RAS, Russia M. Stawiska University of Illinois at Chicago, USA Titles in This Subseries (Continued from the front of this publication)

2 Stephen Gelbart, Roger Howe, and Peter Sarnak, Editors, Festschrift in honor of I. I. Piatetski-Shapiro, part 1: Papers in representation theory, 1990 1 Louis Rowen, Editor, Ring theory, in honor of 8. A. Amitsur, 1989 The papers in this volume cover a wide variety of topics in the geometric theory of func- tions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

ISBN 978-0-8218-4150-1

9 780821 841501