Positivity and Fourier integrals over regular hexagon

JOURNAL OF APPROXIMATION THEORY

卷:207

Article

Xu, Yuan¹ 

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

关键词: Fourier integral;    Hexagon;    Positivity Bochner-Riesz means;    Positive definite function;   

DOI  :  10.1016/j.jat.2016.02.016

来源: Elsevier

【 摘 要 】

Let f epsilon L-1(R-2) and let (f) over cap be its Fourier integral. We study summability of the partial integral S-rho,S-H(x) integral{vertical bar vertical bar y vertical bar vertical bar (H) <= rho}(eix.y) (f) over cap (y)dy, where vertical bar vertical bar y vertical bar vertical bar(H) denotes the uniform norm taken over the regular hexagonal domain. We prove that the Riesz (R, delta) means of the inverse Fourier integrals are nonnegative if and only if delta >= 2. Moreover, we describe a class of vertical bar vertical bar center dot vertical bar vertical bar(H)-radial functions that are positive definite on R-2. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free