# A Brief Introduction to Hilbert Space Theory with RKHS in Mind

*Speaker*:**Aydın Aytuna**
(Emeritus, Affiliated Faculty at the Institute of Applied Mathematics, METU)

*Date / Time*:**Tuesday, March 19, 2024 / 15:40**

*Place*:**S-212 @ IAM** /
**Online Participation** (please self-register first)

**Abstract:** These notes are written for the ‘‘RKHS Learning Seminars’’ at the Institute of Applied Mathematics, METU. It aims to introduce the audience to the fundamental ideas of elementary Hilbert space theory. We assume the participants have good knowledge of linear algebra and advanced calculus. The material covered is relatively standard and contains no new mathematics. The book “A Primer on Reproducing Kernel Hilbert Spaces” by J. H. Manton and P. Amblard (Manton & Amblard, 2015) was chosen as the principal reference for this seminar series. Hence, it shaped the structure of these notes. Additional references used in these notes, plus references that can be used for further studies, are listed below.

*Additional Material*: Lecture Notes of Aydın Aytuna

- Manton, J. H., & Amblard, P.-O. (2015).
*A Primer on Reproducing Kernel Hilbert Spaces*. https://doi.org/10.1561/2000000050

#### Additional References

- H. Aronszajn: Theory of Reproducing Kernels, TAMS Vol. 68, No.3, 1950, pp. 337-404
- E. Kreyszig: Introductory functional analysis with applications, John Wiley & Sons, 1978
- R. Meise, D. Vogt: Introduction to Functional Analysis, Oxford Graduate Texts in Mathematics, Band 2, 1997
- B. Okutmuştur: “A Survey on Hilbert Spaces and Reproducing Kernels” in Functional Calculus, London: Intech Open, 2020, pp 61-77
- V. Paulsen, M. Raghupathi: An introduction to the theory of reproducing kernel Hilbert spaces, Cambridge University Press 2016
- W. Rudin: Functional Analysis, 2. Edition Mc Graw-Hill