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Jump problem and removable singularities for monogenic functions |
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| Authors: | Ricardo Abreu-Blaya Juan Bory-Reyes Dixan Peña-Peña |
| Institution: | (1) Faculty of Mathematics and Informatics, Universidad de Holguín, 80100 Holguín, Cuba;(2) Department of Mathematics, Universidad de Oriente, 90500 Santiago de Cuba, Cuba;(3) Department of Mathematical Analysis, University of Ghent, Galglaan 2, B-9000 Gent, Belgium |
| Abstract: | In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to ℝn+1 (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved. Communicated by Jenny Harrison |
| Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 30E20 30E25 30G35 32D20 |
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