Article ID: MTJPAM-D-21-00058

Title: Stability of Semigroups Defined on Tensor Products of Hilbert Spaces


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00058; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 103-113

Document Type: Research Paper

Author(s): Michael Gil’ a

aDepartment of Mathematics, Ben Gurion University of the Negev, P.0. Box 653, Beer-Sheva 84105, Israel

Received: 7 September 2021, Accepted: 28 January 2022, Published: 28 March 2022.

Corresponding Author: Michael Gil’ (Email address: gilmi@bezeqint.net)

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Abstract

The paper deals with a class of strongly continuous semigroups generated by operators defined on the tensor product of Hilbert spaces. Explicit exponential stability conditions for the considered semigroups are derived. Applications of the obtained conditions to semigroups generated by matrix differential operators and integro-differential operators are also discussed.

Keywords: Hilbert space, Semigroup, Tensor product, Stability, Matrix differential operator, Integro-differential equation

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