- 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
- Reviewed
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