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Assorted Problems

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Book cover Twentieth Century Harmonic Analysis — A Celebration

Part of the book series: NATO Science Series ((NAII,volume 33))

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Abstract

S. Azizi, J-N. McDonald, and D. Cochran, Arizona State University If f ∈ L2(Rd) has compactly supported Fourier transform and 7 : Rd → Rd has the form γ(x;) = Ax + b where A ∈ GLd(R) and b ∈ Rd, then h = f o γ also has compactly supported Fourier transform. It is possible to construct specific f and 7 so that f and f o ∈ both have compactly supported Fourier transforms, f is not the zero function, and ∈ is a continuous and invertible function that is not of the affine form just given. This construction can be accomplished, for example, by considering a d-fold cartesian product of known one- dimensional examples such as described in [1]

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Author information

Authors and Affiliations

  1. Prometheus Inc., Newport, RI, USA

    James S. Byrnes

  2. University of Massachusetts at Boston, Boston, MA, USA

    James S. Byrnes

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  1. James S. Byrnes
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Editor information

Editors and Affiliations

  1. Prometheus Inc., Newport, RI, USA

    James S. Byrnes

  2. University of Massachusetts at Boston, Boston, MA, USA

    James S. Byrnes

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© 2001 Springer Science+Business Media Dordrecht

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Byrnes, J.S. (2001). Assorted Problems. In: Byrnes, J.S. (eds) Twentieth Century Harmonic Analysis — A Celebration. NATO Science Series, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0662-0_16

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  • DOI: https://doi.org/10.1007/978-94-010-0662-0_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7169-4

  • Online ISBN: 978-94-010-0662-0

  • eBook Packages: Springer Book Archive

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