ON THE ORDER OF SUMMABILITY OF THE FOURIER INVERSION FORMULA

作     者：Jasson Vindas Ricardo Estrada 

作者机构：Chent University Belgium Louisiana State University USA 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2010年第26卷第1期

页      面：13-42页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：support by the Louisiana State Board of Regents grant LEQSF(2005-2007)-ENH-TR-21 

主　　题：Fourier inversion formula tempered distribution distributional point value Cesaro summability of Fourier series and integrals summability of distributional evaluations 

摘      要：In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.