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ЖУРНАЛЫ // Проблемы анализа — Issues of Analysis // Архив

Пробл. анал. Issues Anal., 2022, том 11(29), выпуск 1, страницы 67–80 (Mi pa343)

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.

УДК: 517.9, 517.4

MSC: 45D05, 45E05, 46B70, 47D06

Поступила в редакцию: 31.05.2021
Исправленный вариант: 12.11.2021
Принята в печать: 29.11.2021

Язык публикации: английский

DOI: 10.15393/j3.art.2022.10350



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