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)

 

Functions with bounded spectrum


Author: Ha Huy Bang
Journal: Trans. Amer. Math. Soc. 347 (1995), 1067-1080
MSC: Primary 42B10; Secondary 26D20, 46E35
MathSciNet review: 1283539
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ 0 < p \leqslant \infty ,\,f(x) \in {L_p}({\mathbb{R}^n})$, and $ \operatorname{supp} Ff$ be bounded, where $ F$ is the Fourier transform. We will prove in this paper that the sequence $ \vert\vert{D^\alpha }f\vert\vert _p^{1/\vert\alpha \vert},\,\alpha \geqslant 0$, has the same behavior as the sequence $ \mathop {\lim }\limits_{\xi \in \operatorname{supp} Ff} \vert{\xi ^\alpha }{\vert^{1/\vert\alpha \vert}}$, $ \alpha \geqslant 0$. In other words, if we know all "far points" of $ \operatorname{supp} Ff$, we can wholly describe this behavior without any concrete calculation of $ \vert\vert{D^\alpha }f\vert{\vert _p},\,\alpha \geqslant 0$. A Paley-Wiener-Schwartz theorem for a nonconvex case, which is a consequence of the result, is given.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B10, 26D20, 46E35

Retrieve articles in all journals with MSC: 42B10, 26D20, 46E35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1283539-1
PII: S 0002-9947(1995)1283539-1
Keywords: Inequalities for derivatives, Fourier transform
Article copyright: © Copyright 1995 American Mathematical Society