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 Schwarz Problems for Poly-Hardy Space on the Unit Ball
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/17423

title: Schwarz Problems for Poly-Hardy Space on the Unit Ball
authors: Kähler, Uwe
Ku, Min
Qian, Tao
keywords: Hardy space
Schwarz problems
Schwarz kernel
Monogenic signals
issue date: Jun-2017
publisher: Springer Verlag
abstract: In this paper we study the Schwarz boundary value problem for the poly-Hardy space defined on the unit ball of higher dimensional Euclidean space R^n. We first discuss the boundary behavior of functions belonging to the poly-Hardy class. Then we construct the Schwarz kernel function, and describe the boundary properties of the Schwarz-type integrable operator. Finally, we study the Schwarz BVP for the Hardy class and the poly-Hardy class on the unit ball of higher dimensional Euclidean space R^n, and obtain explicit expressions of solutions. As an application, the monogenic signals considered for the Hardy spaces defined on the unit sphere are reconstructed when the scalar- and sub-algebra-valued data are given, which is the extension of the analytic signals for the Hardy spaces on the unit circle of the complex plane.
URI: http://hdl.handle.net/10773/17423
ISSN: 1422-6383
publisher version/DOI: http://dx.doi.org/10.1007/s00025-016-0575-2
source: Results in Mathematics
appears in collectionsCIDMA - Artigos

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