Non-absolutely convergent integrals with respect to distributions View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-10

AUTHORS

Jan Malý

ABSTRACT

We define an integral of a function with respect to a distribution. In case that the underlying distribution is just the Lebesgue measure, the definition leads to a new non-absolutely convergent integral which is wider than the Denjoy–Perron integral. We present a version of the Gauss–Green theorem where the new integral is used for both interior and boundary terms. As a by-product, we characterize the predual Sobolev space . More... »

PAGES

1457-1484

References to SciGraph publications

  • 2006-11. Fluxes Across Parts of Fractal Boundaries in MILAN JOURNAL OF MATHEMATICS
  • 1990. The space of Henstock integrable functions II in NEW INTEGRALS
  • 1936-12. The Perron-Stieltjes integral in MATHEMATISCHE ZEITSCHRIFT
  • 2014-09. Non-absolutely convergent integrals and singular integrals in COLLECTANEA MATHEMATICA
  • 1915-12. Der Perronsche Integralbegriff und seine Beziehung zum Lebesgueschen in MONATSHEFTE FÜR MATHEMATIK
  • 2001. Functional Analysis and Infinite-Dimensional Geometry in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10231-013-0338-6

    DOI

    http://dx.doi.org/10.1007/s10231-013-0338-6

    DIMENSIONS

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