Schwabik, Štefan Operator-valued functions of bounded semivariation and convolutions. (English) Zbl 1001.26005 Math. Bohem. 126, No. 4, 745-777 (2001). Summary: The abstract Perron-Stieltjes integral in the Kurzweil-Henstock sense given via integral sums is used for defining convolutions of Banach space-valued functions. Basic facts concerning integration are presented, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations. MSC: 26A45 Functions of bounded variation, generalizations 26A39 Denjoy and Perron integrals, other special integrals 46G10 Vector-valued measures and integration 26A42 Integrals of Riemann, Stieltjes and Lebesgue type Keywords:Kurzweil-Henstock integration; convolution; Banach space-valued functions; functions of bounded semivariation PDF BibTeX XML Cite \textit{Š. Schwabik}, Math. Bohem. 126, No. 4, 745--777 (2001; Zbl 1001.26005) Full Text: EuDML OpenURL