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Functions on discrete sets holomorphic in the sense of Ferrand, or monodiffric functions of the second kind
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2008 (English)In: Science in China Series A: Mathematics, ISSN 1006-9283, Vol. 51, no 4, 604-619 p.Article in journal (Refereed) Published
Abstract [en]

We study the class of functions called monodiffric of the second kind by Isaacs. They are discrete analogues of holomorphic functions of one or two complex variables. Discrete analogues of the Cauchy-Riemann operator, of domains of holomorphy in one discrete variable, and of the Hartogs phenomenon in two discrete variables are investigated. Two fundamental solutions to the discrete Cauchy-Riemann equation are studied: one with support in a quadrant, the other with decay at infinity. The first is easy to construct by induction; the second is accessed via its Fourier transform.

Place, publisher, year, edition, pages
2008. Vol. 51, no 4, 604-619 p.
Keyword [en]
monodiffric function, holomorphic function on a discrete set, difference operator, Cauchy--Riemann operator, domain of holomorphy, Hartogs phenomenon
National Category
Discrete Mathematics
Research subject
URN: urn:nbn:se:uu:diva-87555DOI: 10.1007/s11425-007-0192-3ISI: 000254626300009OAI: oai:DiVA.org:uu-87555DiVA: diva2:132711
Available from: 2008-12-28 Created: 2008-12-28 Last updated: 2009-11-11Bibliographically approved

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Science in China Series A: Mathematics
Discrete Mathematics

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