Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42A38, 33A55, 44A15

Retrieve articles in all journals with MSC: 42A38, 33A55, 44A15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0951885-1
PII: S 0002-9947(1989)0951885-1
Article copyright: © Copyright 1989 American Mathematical Society