Regular functions of operators on tensor products of Hilbert spaces

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Abstract

A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the mentioned results to integro-differential equations are also discussed.

Original languageEnglish
Pages (from-to)317-331
Number of pages15
JournalIntegral Equations and Operator Theory
Volume54
Issue number3
DOIs
StatePublished - 1 Mar 2006

Keywords

  • Hilbert spaces
  • Integro-differential equations
  • Operator functions
  • Tensor products

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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