Hardy, Paley-Wiener and Bernstein spaces in Clifford analysis

Title: Hardy, Paley-Wiener and Bernstein spaces in Clifford analysis
Creator: Franklin, D. J.; Hogan, J. A.; Larkin, K. G.
Relation: Funding BodyARCGrant NumberDP160101537 http://purl.org/au-research/grants/arc/DP160101537
Relation: Complex Variables and Elliptic Equations Vol. 62, Issue 9, p. 1314-1328
Publisher Link: http://dx.doi.org/10.1080/17476933.2016.1250411
Publisher: Taylor & Francis
Resource Type: journal article
Date: 2017
Description: We describe the relationship between the growth conditions of monogenic extensions of square-integrable functions f in terms of pointwise bounds or bounds on integral averages on the one hand, and the support of the Fourier transform ̂f or its annihilation by certain higher-dimensional analogues of the signum function on the other. We review known results involving a function’s monogenic extension and their classical Fourier transform. These results are extended to the Clifford-Fourier transform of Brackx, De Schepper and Sommen. The equivalence of the pointwise bounds and the bounds on the integral averages is observed as a consequence.
Subject: Paley-Wiener theorem; Hardy spaces; Clifford algebra; Clifford Fourier transform
Identifier: http://hdl.handle.net/1959.13/1399469
Identifier: uon:34607
Identifier: ISSN:1747-6933
Language: eng
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