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

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Abstract: Let , and be bounded, where is the Fourier transform. We will prove in this paper that the sequence , has the same behavior as the sequence , . In other words, if we know all "far points" of , we can wholly describe this behavior without any concrete calculation of . A Paley-Wiener-Schwartz theorem for a nonconvex case, which is a consequence of the result, is given.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1995-1283539-1

Keywords:
Inequalities for derivatives,
Fourier transform

Article copyright:
© Copyright 1995
American Mathematical Society