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The finite part of singular integrals in several complex variables
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
1993 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 337, no 2, 771-793 p.Article in journal (Refereed) Published
Abstract [en]

A divergent integral can sometimes be handled by assigning to it as its value the finite part in the sense of Hadamard. This is done by expanding the integral over the complement of a symmetric neighborhood of a singularity in powers of the radius, and throwing away the negative powers. In this paper the finite part of a singular integral of Cauchy type is defined, and this is then used to describe the boundary behavior of derivatives of a Cauchy-type integral. The finite part of a singular integral of Bochner-Martinelli type is studied, and an extension of the Plemelj jump formulas is shown to hold.

Place, publisher, year, edition, pages
1993. Vol. 337, no 2, 771-793 p.
Identifiers
URN: urn:nbn:se:hig:diva-1185DOI: 10.1090/S0002-9947-1993-1120777-0ISI: A1993LF14600012OAI: oai:DiVA.org:hig-1185DiVA: diva2:117847
Available from: 2008-01-13 Created: 2008-01-13 Last updated: 2011-11-24Bibliographically approved

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Wang, Xiaoqin
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