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On Multivariate Sampling of a Class of Integral Transforms

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Topics in Classical and Modern Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

The Fourier transform plays an important role in many applications, including signal and image processing where the Whittaker–Shannon–Kotelnikov sampling theorem provides a pivotal tool in the analog–digital–analog signal conversion. In this article we discuss some generalizations of the Fourier transform and their associated sampling theorems, such as the fractional Fourier transform, the linear canonical transform, and the special affine Fourier transform. The focus is on the extension of their sampling theorems to higher dimensions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, DePaul University, Chicago, IL, USA

    Ahmed I. Zayed

Authors
  1. Ahmed I. Zayed
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Correspondence to Ahmed I. Zayed .

Editor information

Editors and Affiliations

  1. Georgia Southern University, Statesboro, GA, USA

    Martha Abell

  2. Georgia Southern University, Statesboro, GA, USA

    Emil Iacob

  3. Georgia Southern University, Statesboro, GA, USA

    Alex Stokolos

  4. Georgia Southern University, Statesboro, GA, USA

    Sharon Taylor

  5. ICREA, Passeig de Lluís Companys, Barcelona, Spain ; Centre de Recerca Matemàtica, Barcelona, Spain

    Sergey Tikhonov

  6. Georgia Southern University, Statesboro, GA, USA

    Jiehua Zhu

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Zayed, A.I. (2019). On Multivariate Sampling of a Class of Integral Transforms. In: Abell, M., Iacob, E., Stokolos, A., Taylor, S., Tikhonov, S., Zhu, J. (eds) Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12277-5_22

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