A Survey on Hilbert Spaces and Reproducing Kernels

Date

2020-02-01

Author

Okutmuştur, Baver

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The main purpose of this chapter is to provide a brief review of Hilbert space with its fundamental features and introduce reproducing kernels of the corresponding spaces. We separate our analysis into two parts. In the first part, the basic facts on the inner product spaces including the notion of norms, pre-Hilbert spaces, and finally Hilbert spaces are presented. The second part is devoted to the reproducing kernels and the related Hilbert spaces which is called the reproducing kernel Hilbert spaces (RKHS) in the complex plane. The operations on reproducing kernels with some important theorems on the Bergman kernel for different domains are analyzed in this part.

URI

https://www.intechopen.com/books/functional-calculus
https://hdl.handle.net/11511/71372

Relation

Functional Calculus

Collections

Department of Mathematics, Book / Book chapter

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Citation Formats

B. Okutmuştur, A Survey on Hilbert Spaces and Reproducing Kernels. 2020, p. 77.