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Riemann Boundary Value Problems on the Sphere in Clifford Analysis

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Abstract

We present and study a type of Riemann boundary value problems (for short RBVPs) for polynomially monogenic functions, i.e. null solutions to polynomially generalized Cauchy-Riemann equations, over the sphere of \({\mathbb{R}^{n+1}}\). Making use of Fischer type decomposition and the Clifford calculus for polynomially monogenic functions, we obtain explicit expressions of solutions of this kind of boundary value problems over the sphere of \({\mathbb{R}^{n+1}}\). As special cases the solutions of the corresponding boundary value problems for classical polyanalytic functions and metaanalytic functions are derived respectively.

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Authors and Affiliations

  1. Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Departamento de Matemática, Universidade de Aveiro, P-3810-193, Aveiro, Portugal

    Min Ku & Uwe Kähler

  2. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, P.R. China

    Min Ku & Daoshun Wang

Authors
  1. Min Ku
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  2. Uwe Kähler
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  3. Daoshun Wang
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Corresponding author

Correspondence to Min Ku.

Additional information

The first author was partially supported by Pós-Doutorado Fundaçâo para a Ciência e a Tecnologia of Portugal under Grant No. SFRH/BPD/74581/2010 and Postdoctoral Foundation of China under Grant No. 201003111. The first and second author were partially supported Unidade de Investigação Matemática e Aplicações of the University of Aveiro.

The third author was partially supported by NNSF of China under Grant No. 60873249.

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Ku, M., Kähler, U. & Wang, D. Riemann Boundary Value Problems on the Sphere in Clifford Analysis. Adv. Appl. Clifford Algebras 22, 365–390 (2012). https://doi.org/10.1007/s00006-011-0308-2

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  • DOI: https://doi.org/10.1007/s00006-011-0308-2

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