密度方法在谱与tilings关系中的一个应用  

An application of the density method in the spectra-tilings relations

作　　者：姚海洪[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《纺织高校基础科学学报》2013年第2期208-210,共3页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11171201);陕西省自然科学基金资助项目(2011JM1007)

摘　　要：谱对与tiling对存在某些确定的联系,两者在小波理论、离散Fourier分析与三角逼近理论中有着直接的应用.本文将从谱与tilings的基本性质出发,利用密度方法,得到谱与tilings关系中集合的勒贝格测度的一些估计,为进一步研究此类问题奠定基础.这里的研究是基于谱与tilings的基本性质,与共轭Fuglede猜想密切相关.Spectral pairs have certain relations to tiling pairs. Both have a direct application in the theory of wavelets and in the theory of trigonometric approximation. In the present paper we give an application of the density method in spectra-tilings relations. The research here is based on the fundamental proper- ties of spectra and tilings. By applying the density method, the Lebesgue measure of sets in the spectra-til ings relations is estimated. This is necessary for the further investigate on the relations between spectra and tilings. The research here is based on the fundamental properties of spectra and tilings, and is closely related to the dual Fuglede conjecture.

关 键 词：谱对 tiling对 离散集合 密度 

分 类 号：O177.7[理学—数学]