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Integral resolvent for Volterra equations and Favard spaces
A. Fadilia, F. Maraghb a Laboratory LIMATI, Department of Mathematics and Informatics,
Polydisciplinary Faculty, Sultan Moulay Slimane University,
Mghila, PB 592 Beni Mellal, Morocco
b Laboratory LAMA, Department of Mathematics, Faculty of Science,
Ibn Zohr University, Boîte Postale 32/S Agadir 80000 Souss-Massa, Morocco
Аннотация:
The objective of this work is to give a characterization of the domain $D\left(A\right)$ of $A$ in terms of the integral resolvent family of the equation $x\left(t\right)=x_{0}+\int\limits_{0}^{t}a\left(t-s\right)Ax(s)ds$, $t\geq0$, where $A$ is a linear closed densely defined operator, $a\in L_{loc}^{1}\left(\mathbb{R}^{+}\right)$ in a general Banach space $X$ and $ x_{0}\in X $. Furthermore, we give a relationship between the Favard classes (temporal and frequency) for integral resolvents.
Ключевые слова:
semigroups, scalar Volterra integral equations, integral resolvent families, Favard spaces.
Поступила в редакцию: 31.05.2021 Исправленный вариант: 12.11.2021 Принята в печать: 29.11.2021
Образец цитирования:
A. Fadili, F. Maragh, “Integral resolvent for Volterra equations and Favard spaces”, Пробл. анал. Issues Anal., 11(29):1 (2022), 67–80
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pa343 https://www.mathnet.ru/rus/pa/v29/i1/p67
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