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
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: firstname.lastname@example.org)
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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 equationReferences:
- D. Andrica and Th. M. Rassias (eds.), Differential and integral inequalities, Springer Optimization and Its Applications 151, Springer Nature, Switzerland, 2019.
- W. Arendt, C. J. K. Batty, F. Neubrander and M. Hieber, Laplace transforms and Cauchy problems, Springer, Basel, 2011.
- J. W. Brewer, Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits Syst. 25, 772–781, 1978.
- A. Brown and C. Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17, 162–166, 1966.
- R. Curtain and H. Zwart, Introduction to infinite-dimensional systems theory, Springer, New York, 1995.
- N. Dunford and J. T. Schwartz, Linear operators, part I. General Theory. Wiley Interscience publishers, New York, 1966.
- T. Eisner, Stability of operators and operator semigroups, Operator Theory: Advances and Applications Vol. 209, Birkhauser Verlag, Basel, 2010.
- K.-J. Engel and R. Nagel, A short course on operator semigroups, Universitext. Springer, New York, 2006.
- M. I. Gil’, Spectrum and resolvent of a partial integral operator, Appl. Anal. 87 (5), 555–566, 2008.
- M. I. Gil’, Perturbations of operators on tensor products and spectrum localization of matrix differential operators, J. Appl. Funct. Anal. 3 (3), 315–332, 2008.
- M. I. Gil’, Operator functions and operator equations, World Scientific, New Jersey, 2018.
- M. I. Gil’, Semigroups of sums of two operators with small commutators, Semigroup Forum 98 (1), 22–30, 2019.
- P. M. Pardalos and Th. M. Rassias (eds.), Mathematics without boundaries, Surveys in Interdisciplinary Research, VIII , Springer, New York, 2014.
- P. M. Pardalos and Th. M. Rassias (eds.), Contributions in mathematics and engineering, International Publishing, Switzerland, 2016.
- Th. M. Rassias and V. A. Zagrebnov (eds.), Analysis and operator theory, Springer, New York, 2019.