Email this article Two parameter $C_{0}$-semigroups of linear operators on locally convex spaces
- Authors: Ettayb J.1
-
Affiliations:
- Regional Academy of Education and Training Casablanca–Settat, Hamman Al–Fatawaki Collegiate High School
- Issue: Vol 30, No 150 (2025)
- Pages: 183-204
- Section: Original articles
- URL: https://ogarev-online.ru/2686-9667/article/view/298095
- ID: 298095
Cite item
Full Text
Abstract
The purpose of this paper is to study two parameter (resp. $n$-parameter) expo\-nen\-tial\-ly equicontinuous $C_{0}$-semigroups of continuous linear operators on sequentially complete locally convex Hausdorff spaces. In particular, we demonstrate the Hille--Yosida theorem for two parameter (resp. $n$-parameter) exponentially equicontinuous $C_{0}$-semigroups of continuous linear operators on sequentially complete locally convex Hausdorff spaces. Moreover, the $n$-parameter $C_{0}$-semigroups of continuous linear operators on Banach spaces are studied.
About the authors
Jawad Ettayb
Regional Academy of Education and Training Casablanca–Settat, Hamman Al–Fatawaki Collegiate High School
Author for correspondence.
Email: jawad.ettayb@gmail.com
ORCID iD: 0000-0002-4819-943X
Doctor of Mathematics, Professor at Hamman Al–Fatawaki Collegiate High School
Morocco, Road to Berrechid, Had Soualem 26402, MoroccoReferences
- N.H. Abdelaziz, "Commutativity and generation of n-parameter semigroups of bounded linear operators", Houston Journal of Mathematics, 9:2 (1983), 151-156.
- Sh. Al-Sharif, R. Khalil, "On the generator of two parameter semigroups", Appl. Math. Comput., 156:2 (2004), 403-414.
- H.F. Trotter, "On the product of semigroups of operators", Proceedings of the American Mathematical Society, 10:4 (1959), 545-551.
- V.A. Babalola, "Semigroups of operators on locally convex spaces", Transactions of the American Mathematical Society, 199 (1974), 163-179.
- S. Ouchi, "Semi-groups of operators in locally convex spaces", Journal of the Mathematical Society of Japan, 25:2 (1973), 265-276.
- H. Komatsu, "Semi-groups of operators in locally convex spaces", Journal of the Mathematical Society of Japan, 16:3 (1964), 230-262.
- T. Komura, "Semigroups of operators in locally convex spaces", Journal of Functional Analysis, 2:3 (1968), 258-296.
- L. Naciri, E. Beckenstein, Topological Vector Spaces, 2-nd ed., Taylor & Francis Group, Boca Raton-London-New York, 2011.
- T. Granucci, "Integrated Semigroups on Fréchet space I: Bochner integral, Laplace integral and real representation theorem", Journal of Mathematics Research, 11:1 (2019), 118-143.
- Y.H. Choe, "C_0-semigroups on a locally convex space", J. Math. Anal. Appl., 106:2 (1985), 293-320.
- K. Singbal-Vedak, "Semigroups of operators on a locally convex space", Commentationes Mathematicae, 16:1 (1972), 53-74.
- J. Ettayb, "A Hille-Yosida theorem for two parameter equicontinuous C_0-semigroups on locally convex spaces", Novi Sad J. Math. (to appear).
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. V. 44, Applied Mathematical Sciences, Springer-Verlag, New York, 1983.
Supplementary files
