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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Band-limited functions: $ L\sp p$-convergence


Authors: Juan A. Barceló and Antonio Córdoba
Journal: Trans. Amer. Math. Soc. 313 (1989), 655-669
MSC: Primary 42A38; Secondary 33A55, 44A15
MathSciNet review: 951885
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Abstract: We consider the set $ {B_p}(\Omega)$ (functions of $ {L^p}({\mathbf{R}})$ whose Fourier spectrum lies in $ [ - \Omega , + \Omega ]$). We prove that the prolate spheroidal wave functions constitute a basis of this space if and only if $ 4/3 < p < 4$. The result is obtained as a consequence of the analogous problem for the spherical Bessel functions. The proof rely on a weighted inequality for the Hilbert transform.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0951885-1
Article copyright: © Copyright 1989 American Mathematical Society