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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, 3810-193, Aveiro, Portugal

    Paula Cerejeiras, Uwe Kähler & Min Ku

Authors
  1. Paula Cerejeiras
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  2. Uwe Kähler
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  3. Min Ku
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Correspondence to Min Ku.

Additional information

This work was supported by FEDER funds through COMPETE–Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”), by Portuguese founds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 and by NNSF of China under Grant No. 61170032. The first author is the recipient of Postdoctoral Foundation from FCT (Portugal) under Grant No. SFRH/BPD/74581/2010 and from China under Grant No. 201003111.

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Cerejeiras, P., Kähler, U. & Ku, M. On the Riemann Boundary Value Problem for Null Solutions to Iterated Generalized Cauchy–Riemann Operator in Clifford Analysis. Results. Math. 63, 1375–1394 (2013). https://doi.org/10.1007/s00025-012-0274-6

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  • DOI: https://doi.org/10.1007/s00025-012-0274-6

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