Synopses & Reviews
This work is the first contributed volume on reproducing kernels and their applications. It is made up of chapters based on presentations at the University of Delaware ISAAC Conference as well as invited contributions by leading experts. Audience: Researchers working in the field as well as scientists interested in the applications.
Synopsis
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 contri- 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.
Table of Contents
Preface.
1. Operator theoretical classification of reproducing kernal Hilbert spaces;
S. Akashi. 2. Holomorphic factorization of matrices of polynomials;
J.P. D'Angelo. 3. Bergman-Carleson measures and Bloch functions on strongly pseudoconvex domains;
H. Arai. 4. The role of the Ahlfors mapping in the theory of kernel functions in the plane;
S.R. Bell. 5. Some generalized Laplace transformations;
E.A.K. Brüning. 6. Asymptotic behaviour of reproducing kernels, Berezin quantization and mean-value theorems;
M. Englis. 7. Hilbert spaces of eigenfunctions of the Laplacian;
K. Fujita. 8. An expansion theorem for state space of unitary linear system whose transfer function is a Riemann mapping function;
S. Ghosechowdhury. 9. The Bergman kernel and a generalized Fourier-Borel transform;
F. Haslinger. 10. The Bergman kernel on certain decoupled domains;
J. Kamimoto. 11. A sampling theorem for solutions of the Dirichlet problem for the Schrödinger operator;
A. Kheyfits. 12. Multi-power Legendre Series in
C^{m};
P.A. McCoy. 13. An essay on the Bergman metric and balanced domains;
T. Ohsawa. 14. Integral transforms involving smooth functions;
S. Saitoh, M. Yamamoto. 15. Applications of the general theory of reproducing kernels;
S. Saitoh. 16. A survey of the extended interpolation;
S. Takahashi. 17. The Nehari problem for the weighted Szego kernels;
M. Uehara. 18. Fay's trisecant formula and Hardy
H^{2} reproducing kernels;
A. Yamada.