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Operator-valued functions of bounded semivariation and convolutions. (English) Zbl 1001.26005

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
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