MATHEMATICA BOHEMICA, Vol. 126, No. 4, pp. 745-777 (2001)

Operator-valued functions of bounded semivariation and convolutions

Stefan Schwabik

Stefan Schwabik, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:

Abstract: 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 preseted, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations.

Keywords: Kurzweil-Henstock integration, convolution, Banach space

Classification (MSC2000): 26A45, 26A42, 46G12

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