Displaying similar documents to “The abstract renewal equation.”

Operator-valued functions of bounded semivariation and convolutions

Štefan Schwabik (2001)

Mathematica Bohemica

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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.

A note on integration by parts for abstract Perron-Stieltjes integrals

Štefan Schwabik (2001)

Mathematica Bohemica

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Integration by parts results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration based on Riemann type integral sums, which leads to the Perron integral.