Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spa...

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Bibliographic Details
Main Author: Castro, L. P. (author)
Other Authors: Saitoh, S. (author), Yamada, A. (author)
Format: article
Language:eng
Published: 2018
Subjects:
Reproducing kernel
Moore-Penrose generalized inverse
Tikhonov regularization
Hilbert-Schmidt operator
Tensor product of Hilbert spaces
Generalized fractional function
Bergman space
Szegö space
Multiplication operator
Online Access:http://hdl.handle.net/10773/16216
Country:Portugal
Oai:oai:ria.ua.pt:10773/16216
Description
Summary:We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

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