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9783764371456

Quadrature Domains And Applications

by
  • ISBN13:

    9783764371456

  • ISBN10:

    3764371455

  • Format: Hardcover
  • Copyright: 2005-03-30
  • Publisher: Birkhauser

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Summary

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.

Table of Contents

Preface vii
Selected Bibliography of Harold S. Shapiro ix
Open Problems Related to Quadrature Domains xi
What is a Quadrature Domain?
1(26)
B. Gustafsson
H.S. Shapiro
Recent Progress and Open Problems in the Bergman Space
27(34)
A. Aleman
H. Hedenmalm
S. Richter
The Bergman Kernel and Quadrature Domains in the Plane
61(18)
S. R. Bell
The Cauchy Transform
79(34)
J.A. Cima
A. Matheson
W.T. Ross
Quadrature Domains and Fluid Dynamics
113(18)
D. Crowdy
On Uniformly Discrete Sequences in the Disk
131(20)
P. Duren
A. Schuster
D. Vukotic
Algebraic Aspects of the Dirichlet Problem
151(22)
P. Ebenfelt
D. Khavinson
H.S. Shapiro
Linear Analysis of Quadrature Domains. IV
173(22)
B. Gustafsson
M. Putinar
Restriction, Localization and Microlocalization
195(12)
M. Sakai
Quadrature Domains and Brownian Motion (A Heuristic Approach)
207(10)
H. Shahgholian
Weighted Composition Operators Associated with Conformal Mappings
217(22)
S. Shimorin
Quadrature Identities and Deformation of Quadrature Domains
239(18)
T. Sjodin
Subharmonicity of Higher Dimensional Exponential Transforms
257
V.G. Tkachev

Supplemental Materials

What is included with this book?

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