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One-sided band-limited approximations of some radial functions

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Abstract

We construct majorants and minorants of a Gaussian function in Euclidean space that have Fourier transforms supported in a box. The majorants that we construct are shown to be extremal and our minorants are shown to be asymptotically extremal as the sides of the box become uniformly large. We then adapt the Distribution and Gaussian Subordination methods of [12] to the multidimensional setting to obtain majorants and minorants for a class of radial functions. Periodic analogues of the main results are proven and applications to Hilbert-type inequalities are given.

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Authors and Affiliations

  1. IMPA–Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, BRAZIL

    Felipe Gonçalves & Jose Madrid

  2. Department of Mathematics, Univ. of Texas 1 University Sta. C1200 Austin, Texas, 78712, USA

    Michael Kelly

Authors
  1. Felipe Gonçalves
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  2. Michael Kelly
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  3. Jose Madrid
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Correspondence to Michael Kelly.

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Gonçalves, F., Kelly, M. & Madrid, J. One-sided band-limited approximations of some radial functions. Bull Braz Math Soc, New Series 46, 563–599 (2015). https://doi.org/10.1007/s00574-015-0104-z

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  • DOI: https://doi.org/10.1007/s00574-015-0104-z

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