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Integral kernels for k-hypermonogenic functions

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Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalComplex Variables and Elliptic Equations
Issue number9
Early online date21 Feb 2017
Publication statusPublished - 2017
Publication typeA1 Journal article-refereed


We consider the modified Cauchy–Riemann operator (Formula presented.) in the universal Clifford algebra (Formula presented.) with the basis (Formula presented.). The null-solutions of this operator are called k-hypermonogenic functions. We calculate the k-hyperbolic harmonic fundamental solutions, i.e. solutions to (Formula presented.), and use these solutions to find k-hypermonogenic kernels for a Cauchy-type integral formula in the upper half-space.


  • Cauchy integral formula, Clifford algebra, hyperbolic Laplace–Beltrami, k-hyperbolic harmonic, k-hypermonogenic

Publication forum classification

Field of science, Statistics Finland