ON KURZWEIL-STIELTJES INTEGRAL IN A BANACH SPACE

Autor(es)

Monteiro, Giselle A. ; Tvrdy, Milan

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICA BOHEMICA; v. 137, n. 4, p. 17-pg., 2012-01-01.

Resumo

In the paper we deal with the Kurzweil-Stieltjes integration of functions having values in a Banach space X. We extend results obtained by Stefan Schwabik and complete the theory so that it will be well applicable to prove results on the continuous dependence of solutions to generalized linear differential equations in a Banach space. By Schwabik, the integral integral(b)(a) d[f] g exists if F : [a, b] L (X) has a bounded semi-variation on [a, b] and g : [a,b] X is regulated on [a, b]. We prove that this integral has sense also if F is regulated on [a, b] and g has a bounded semi-variation on [a, b]. Furthermore, the integration by parts theorem is presented under the assumptions not covered by Schwabik (2001) and Naralenkov (2004), and the substitution formula is proved. (AU)

• Processo FAPESP: 10/52215-2 - Milan Tvrdý | Academy of Sciences of the Czech Republic - República Tcheca
• Beneficiário: Márcia Cristina Anderson Braz Federson
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional