Geodesic
Integral resolvent for Volterra equations and Favard spaces
Problemy analiza, Tome 11 (2022) no. 1, pp. 67-80

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: semigroups, scalar Volterra integral equations, integral resolvent families
Mots-clés : Favard spaces. 
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A. Fadili; F. Maragh. Integral resolvent for Volterra equations and Favard spaces. Problemy analiza, Tome 11 (2022) no. 1, pp. 67-80. http://geodesic.mathdoc.fr/item/PA_2022_11_1_a5/