Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.
Author(s): Peter Ebenfelt, Bjorn Gustafsson, Dmitry Khavinson, Mihai Putinar (Editors)
Edition: 1
Year: 2005
Language: English
Pages: 298
Tags: Математика;Функциональный анализ;Теория операторов;
Cover......Page 1
Operator Theory: Advances and
Applications
Vol. 156......Page 3
Quadrature Domains
and Their Applications......Page 4
ISBN 3764371455......Page 5
Contents......Page 6
Preface......Page 8
Selected Bibliography of Harold S. Shapiro......Page 10
Open Problems Related to
Quadrature Domains......Page 12
What is a Quadrature Domain?......Page 30
Recent Progress and Open Problems
in the Bergman Space......Page 55
The Bergman Kernel and Quadrature Domains
in the Plane......Page 88
The Cauchy Transform......Page 106
Quadrature Domains and Fluid Dynamics......Page 139
On Uniformly Discrete Sequences in the Disk......Page 156
Algebraic Aspects of the Dirichlet Problem......Page 176
Linear Analysis of Quadrature Domains. IV......Page 198
Restriction, Localization and Microlocalization......Page 220
Quadrature Domains and Brownian Motion
(A Heuristic Approach)......Page 231
Weighted Composition Operators
Associated with Conformal Mappings......Page 240
Quadrature Identities and Deformation
of Quadrature Domains......Page 261
Subharmonicity of Higher Dimensional
Exponential Transforms......Page 278
