Displaying similar documents to “A note on integration by parts for abstract Perron-Stieltjes integrals”

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.

The abstract renewal equation.

Schwabik, Štefan (2000)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Substitution formulas for the Kurzweil and Henstock vector integrals

Márcia Federson (2002)

Mathematica Bohemica

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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and...