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Paley-Wiener and Boas Theorems for the Quaternion Fourier Transform

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Abstract

This paper establishes a real Paley-Wiener theorem to characterize the quaternion-valued functions whose quaternion Fourier transform has compact support by the partial derivative and also a Boas theorem to describe the quaternion Fourier transform of these functions that vanish on a neighborhood of the origin by an integral operator.

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Computer Science, Hubei University, Hubei, 430062, China

    Yingxiong Fu & Luoqing Li

Authors
  1. Yingxiong Fu
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  2. Luoqing Li
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Correspondence to Yingxiong Fu.

Additional information

The research was partially supported by NSFC under grant 11071058.

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Fu, Y., Li, L. Paley-Wiener and Boas Theorems for the Quaternion Fourier Transform. Adv. Appl. Clifford Algebras 23, 837–848 (2013). https://doi.org/10.1007/s00006-013-0412-6

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  • DOI: https://doi.org/10.1007/s00006-013-0412-6

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