Band-limited functions: $L^ p$-convergence
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- by Juan A. Barceló and Antonio Córdoba PDF
- Trans. Amer. Math. Soc. 313 (1989), 655-669 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 313 (1989), 655-669
- MSC: Primary 42A38; Secondary 33A55, 44A15
- DOI: https://doi.org/10.1090/S0002-9947-1989-0951885-1
- MathSciNet review: 951885