Quadrature Domains and Their Applications The Harold S. Shapiro Anniversary Volume /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Ebenfelt, Peter (Editor), Gustafsson, Björn (Editor), Khavinson, Dmitry (Editor), Putinar, Mihai (Editor)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2005.
• Series: Operator Theory: Advances and Applications ; 156
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Operator theory.; Numerical analysis.; Physics.; Analysis.; Operator Theory.; Numerical Analysis.; Mathematical Methods in Physics.; Theoretical, Mathematical and Computational Physics.

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 th...

Table of Contents:

• What is a Quadrature Domain?
• Recent Progress and Open Problems in the Bergman Space
• The Bergman Kernel and Quadrature Domains in the Plane
• The Cauchy Transform
• Quadrature Domains and Fluid Dynamics
• On Uniformly Discrete Sequences in the Disk
• Algebraic Aspects of the Dirichlet Problem
• Linear Analysis of Quadrature Domains. IV
• Restriction, Localization and Microlocalization
• Quadrature Domains and Brownian Motion (A Heuristic Approach)
• Weighted Composition Operators Associated with Conformal Mappings
• Quadrature Identities and Deformation of Quadrature Domains
• Subharmonicity of Higher Dimensional Exponential Transforms.