A note on band-limited minorants of an Euclidean ball
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Abstract:
We study the Beurling-Selberg problem of finding band-limited $L^1$-functions that lie below the indicator function of an Euclidean ball. We compute the critical radius of the support of the Fourier transform for which such construction can have a positive integral.References
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Additional Information
- Felipe Gonçalves
- Affiliation: Mathematical and Statistical Sciences, University of Alberta, CAB 632, Edmonton, Alberta, T6G 2G1 Canada
- Email: felipe.goncalves@ualberta.ca
- Received by editor(s): May 2, 2017
- Received by editor(s) in revised form: July 3, 2017
- Published electronically: December 12, 2017
- Communicated by: Harold P. Boas
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2063-2068
- MSC (2010): Primary 42B35; Secondary 33C10
- DOI: https://doi.org/10.1090/proc/13877
- MathSciNet review: 3767357