Speaker: Baver Okutmuştur (Department of Mathematics, METU)

Date / Time: Thursday, April 25, 2024 / 14:00 (Ankara, Turkey)

Place: Online Participation (please self-register first, if necessary)

Abstract: In this talk a short introduction to reproducing kernel and reproducing kernel Hilbert spaces (RKHS) is provided. We first memorize a brief overview of the Hilbert space with its fundamental characteristics. Here the basic facts on the inner product spaces including the notion of norms, pre-Hilbert spaces, and hence Hilbert spaces are briefly presented (for further details see [3]). The main part is then devoted to the definitions and fundamental properties of reproducing kernels and RKHSs. The proofs of most of the theorems are addressed to the lecture notes [1] of T. Ando, the paper [2] of N. Aronszajn and particularly the recent book [5] of S. Saitoh and Y. Sawano.

References:

  1. T. Ando, Reproducing Kernel Spaces and Quadratic Inequalities, Lecture Notes, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics, Sapporo, Japan, 1987.
  2. N. Aronszajn, Theory of reproducing kernels, TAMS Vol. 68, No.3, 1950, pp. 337-404.
  3. J.B. Conway, A Course in Functional Analysis, Springer Verlag, Berlin - Heidelberg - New York, 1989.
  4. P.L. Duren, A. Schuster, Bergman Spaces, Amer. Math. Soc., Providence R.I. 2004.
  5. S. Saitoh, Y. Sawano, Theory of Reproducing Kernels and Applications Springer, 2016. (You may possibly download the book from Springer)

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