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Title: Schwarz Problems for Poly-Hardy Space on the Unit Ball
Author: 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.
Peer review: yes
DOI: 10.1007/s00025-016-0575-2
ISSN: 1422-6383
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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