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Reproducing Kernels and their Applications : International Society for Analysis, Applications and Computation - S. Saitoh

Reproducing Kernels and their Applications

International Society for Analysis, Applications and Computation

By: S. Saitoh (Editor), Daniel Alpay (Editor), Joseph A. Ball (Editor), Takeo Ohsawa (Editor)

Hardcover Published: 30th April 1999
ISBN: 9780792356189
Number Of Pages: 235

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The First International Congress of the International Society for Analysis, its Applications and Computations (ISAAC'97) was held at the University of Delaware from 3 to 7 June 1997. As specified in the invitation of the President Professor Robert P. Gilbert of the ISAAC, we organized the session on Reproducing Kerneis and Their Applications. In our session, we presented 24 engaging talks on topics of current interest to the research community. As suggested and organized by Professor Gilbert, we hereby publish its Proceedings. Rather than restricting the papers to Congress participants, we asked the Ieading mathematicians in the field of the theory of reproducing kern eIs to submit papers. However, due to time restrietions and a compulsion to limit the Proceedings a reasonable size, we were unable to obtain a comprehensive treatment of the theory of reproducing kernels. Nevertheless, we hope this Proceedings of the First International Conference on reproducing kerneis will become a significant reference volume. Indeed, we believe that the theory of reproducing kernels will stand out as a fundamental and beautiful contribution in mathematical sciences with a broad array of applications to other areas of mathematics and science. We would like to thank Professor Robert Gilbert for his substantial contriĀ­ bu tions to the Congress and to our Proceedings. We also express our sincere thanks to the staff of the University of Delaware for their manifold cooperation in organizing the Congress.

Preface
Operator theoretical classification of reproducing kernel Hilbert spacesp. 1
Holomorphic factorization of matrices of polynomialsp. 9
Bergman-Carleson measures and Bloch functions on strongly pseudoconvex domainsp. 21
The role of the Ahlfors mapping in the theory of kernel functions in the planep. 33
Some generalized Laplace transformationsp. 43
Asymptotic behaviour of reproducing kernels, Berezin quantization and mean-value theoremsp. 53
Hilbert spaces of eigenfunctions of the Laplacianp. 65
An expansion theorem for state space of unitary linear system whose transfer function is a Riemann mapping functionp. 81
The Bergman kernel and a generalized Fourier-Borel transformp. 97
The Bergman kernel on certain decoupled domainsp. 109
A sampling theorem for solutions of the Dirichlet problem for the Schrodinger operatorp. 125
Multi-power Legendre series in C[superscript m]p. 133
An essay on the Bergman metric and balanced domainsp. 141
Integral transforms involving smooth functionsp. 149
Applications of the general theory of reproducing kernelsp. 165
A survey of the extended interpolationp. 189
The Nehari problem for the weighted Szego kernelsp. 213
Fay's trisecant formula and Hardy H[superscript 2] reproducing kernelsp. 223
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792356189
ISBN-10: 0792356187
Series: International Society for Analysis, Applications and Computation
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 235
Published: 30th April 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 1.91
Weight (kg): 1.16

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