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On the Supports of Functions Associated to the Radially Deformed Fourier Transform

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Abstract

In recent work a radial deformation of the Fourier transform in the setting of Clifford analysis was introduced. The key idea behind this deformation is a family of new realizations of the Lie superalgebra \({\mathfrak {osp}}(1|2)\) in terms of a so-called radially deformed Dirac operator \({\mathbf {D}}\) depending on a deformation parameter c such that for \(c=0\) the classical Dirac operator is reobtained. In this paper, several versions of the Paley–Wiener theorems for this radially deformed Fourier transform are investigated, which characterize the supports of functions associated to this generalized Fourier transform in Clifford analysis.

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Authors and Affiliations

  1. School of Mathematics, Southwest Minzu University, Chengdu, 610041, People’s Republic of China

    Shanshan Li

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Jinsong Leng & Minggang Fei

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  1. Shanshan Li
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  2. Jinsong Leng
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  3. Minggang Fei
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Correspondence to Minggang Fei.

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The authors were partially supported by “the Fundamental Research Funds for the Central Universities” with no. ZYGX2019J091.

This article is part of the Topical Collection on ISAAC 12 at Aveiro, July 29–August 2, 2019, edited by Swanhild Bernstein, Uwe Kaehler, Irene Sabadini, and Franciscus Sommen.

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Li, S., Leng, J. & Fei, M. On the Supports of Functions Associated to the Radially Deformed Fourier Transform. Adv. Appl. Clifford Algebras 30, 47 (2020). https://doi.org/10.1007/s00006-020-01067-7

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  • DOI: https://doi.org/10.1007/s00006-020-01067-7

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