Reproducing Kernels and their Applications

1. Front Matter

   Pages i-vii

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2. Operator Theoretical Classification of Reproducing Kernel Hilbert Spaces

   • Shigeo Akashi

   Pages 1-7

3. Holomorphic Factorization of Matrices of Polynomials

   • John P. D’Angelo

   Pages 9-19

4. Bergman-Carleson Measures and Bloch Functions on Strongly Pseudoconvex Domains

   • Hitoshi Arai

   Pages 21-31

5. The Role of the Ahlfors Mapping in the Theory of Kernel Functions in the Plane

   • Steven R. Bell

   Pages 33-42

6. Some Generalized Laplace Transformations

   • Erwin A. K. Brüning

   Pages 43-51

7. Asymptotic Behaviour of Reproducing Kernels, Berezin Quantization and Mean-Value Theorems

   • Miroslav Engliš

   Pages 53-64

8. Hilbert Spaces of Eigenfunctions of the Laplacian

   • Keiko Fujita

   Pages 65-80

9. An Expansion Theorem for State Space of Unitary Linear System Whose Transfer Function is a Riemann Mapping Function

   • Subhajit Ghosechowdhury

   Pages 81-95

10. The Bergman Kernel and a Generalized Fourier-Borel Transform

    • Friedrich Haslinger

    Pages 97-108

11. The Bergman Kernel on Certain Decoupled Domains

    • Joe Kamimoto

    Pages 109-124

12. A Sampling Theorem for solutions of the Dirichlet Problem for the Schrödinger Operator

    • Alexander Kheyfits

    Pages 125-131

13. Multi-power Legendre Series in C ^m

    • Peter A. McCoy

    Pages 133-140

14. An Essay on the Bergman Metric and Balanced Domains

    • Takeo Ohsawa

    Pages 141-148

15. Integral Transforms Involving Smooth Functions

    • Saburou Saitoh, Masahiro Yamamoto

    Pages 149-163

16. Applications of the General Theory of Reproducing Kernels

    • Saburou Saitoh

    Pages 165-188

17. A Survey of the Extended Interpolation

    • Sechiko Takahashi

    Pages 189-212

18. The Nehari problem for the weighted Szegő kernels

    • Masahiro Uehara

    Pages 213-221

19. Fay’s Trisecant Formula and Hardy H ² Reproducing Kernels

    • Akira Yamada

    Pages 223-234

20. Back Matter

    Pages 235-235

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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 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.

• Factor
• Hilbert space
• Pseudoconvexity
• Volume
• behavior
• field
• form
• functions
• interpolation
• kernel
• operator
• schrödinger operator
• system
• transformation
• university
• partial differential equations

• Gunma University, Japan

  Saburou Saitoh

• Ben-Gurion University, Israel

  Daniel Alpay

• Virginia Tech, USA

  Joseph A. Ball

• Nagoya University, Japan

  Takeo Ohsawa

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