NDLI: On the Riemann Boundary Value Problem for Null Solutions to Iterated Generalized Cauchy

Content Provider	Springer Nature Link
Author	Ku, Min Kähler, Uwe Cerejeiras, Paula
Copyright Year	2012
Abstract	In this paper we consider a kind of Riemann boundary value problem (for short RBVP) for null solutions to the iterated generalized Cauchy–Riemann operator and the polynomially generalized Cauchy–Riemann operator, on the sphere of $${\mathbb{R}^{n+1}}$$ with Hölder-continuous boundary data. Making full use of the poly-Cauchy type integral operator in Clifford analysis, we give explicit integral expressions of solutions to this kind of boundary value problems over the sphere of $${\mathbb{R}^{n+1}}$$ . As special cases solutions of the corresponding boundary value problems for the classical poly-analytic and meta-analytic functions are also derived, respectively.
Ending Page	1394
Page Count	20
Starting Page	1375
File Format	PDF
ISSN	14226383
e-ISSN	14209012
Journal	Results in Mathematics
Issue Number	3
Volume Number	63
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2012-08-18
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized Cauchy–Riemann operator Functions of hypercomplex variables and generalized variables Integral representations; canonical kernels (SzegÃ…, Bergman, etc.) Clifford analysis Representations of entire functions by series and integrals Poly-Cauchy type integral Riemann boundary value problems Differential forms Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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On the Riemann Boundary Value Problem for Null Solutions to Iterated Generalized Cauchy–Riemann Operator in Clifford Analysis