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Hilbert transforms and the Cauchy integral in euclidean space
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 193, no 2, 161-187 p.Article in journal (Refereed) Published
Abstract [en]

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher-dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class of generalized double layer potential operators on Lipschitz surfaces and boundedness of related Hilbert transforms.

Place, publisher, year, edition, pages
2009. Vol. 193, no 2, 161-187 p.
Keyword [en]
Cauchy integral, Dirac equation, double layer potential, Hilbert transform, harmonic conjugates, Lipschitz domain
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-59665DOI: 10.4064/sm193-2-4ISI: 000271387800004OAI: oai:DiVA.org:su-59665DiVA: diva2:432137
Note
authorCount :3Available from: 2011-08-01 Created: 2011-07-05 Last updated: 2017-12-08Bibliographically approved

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