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Complex Analysis and Operator Theory

, Volume 10, Issue 8, pp 1705–1723 | Cite as

Solutions of Tikhonov Functional Equations and Applications to Multiplication Operators on Szegö Spaces

  • L. P. CastroEmail author
  • S. Saitoh
  • A. Yamada
Article
  • 154 Downloads

Abstract

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.

Keywords

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 

Mathematics Subject Classification

47A52 46E22 30C40 32A36 47A15 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal
  2. 2.Institute of Reproducing KernelsKiryuJapan
  3. 3.Department of MathematicsTokyo Gakugei UniversityTokyoJapan

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