No characterization of generators in lP (1<p<2) by zero set of Fourier transform

被引：2

作者：

Lev, Nir ^{[1
]}

Olevskii, Alexander ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

COMPTES RENDUS MATHEMATIQUE | 2008年 / 346卷 / 11-12期

关键词：

D O I：

10.1016/j.crma.2008.04.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given 1 < p < 2 we construct two continuous functions f and g on the circle, with the following properties: (i) They have the same set of zeros; (ii) The Fourier transforms (f) over cap and (g) over cap both belong to l(p)(Z); (iii) The translates of (g) over cap span the whole l(p), but those of f do not. A similar result is true for LP(R). This should be contrasted with the Wiener theorems related to p = 1, 2.

引用

页码：645 / 648

页数：4

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No characterization of generators in lP (1&lt;p&lt;2) by zero set of Fourier transform

No characterization of generators in lP (1<p<2) by zero set of Fourier transform