空间自仿测度下无限正交指数系存在的条件及谱性质的分析
发布时间：2018-07-16 13:49
【摘要】：自仿测度μM,D的谱与非谱问题是自仿测度谱理论研究的主要内容之一而μM,D-正交指数系的有限性或无限性问题在研究自仿测度是否为谱测度中起着重要的作用.因此,本文主要针对空间自仿测度下无限正交指数函数系存在的条件及谱性质进行分析,得到如下研究结果：第一部分,通过利用函数mD(x)零点集Z(mD)中的非零中间点(即坐标为0或1/2的点)的性质,得到空间自仿测度下无限μM,D-正交指数函数系存在的许多条件,为进一步研究空间自仿测度μM,D的谱性质奠定基础.同时,给出这些结论的一些应用.第二部分,主要对三维空间R3中当M=1/2[p1+p2,p1-p3,p2-p3; p1-p2,p1+p3,-p2+p3;-p1+p2,-p1+p3,p2+p3],D={0,e1,e2,e3}时,其中pj∈Z\{0,±1}(j=1,2,3),e1,e2,e3是R3中的单位向量,自仿测度μM,D的谱性质进行分析,得到的结果是(1)当pj∈2Z\{0,2}(j=1,2,3)或p1=p2=p3=2时,μM.D是谱测度；(2)当p1,p2,p3这三个数中至少有一个数是偶数时,空间L2(μM,D)中存在无限正交系E(A)且A(?)Z3；(3)当pj∈2Z+1\(±1}(j=1,2,3)时,PM,D不是谱测度,且空间L2(μM,D)中正交指数函数系至多包含“4”个元素,且数字“4”是最好的.
[Abstract]:The spectral and non-spectral problems of the self-imitating measure 渭 Mn-D are one of the main contents in the study of the spectrum theory of the self-imitating measure, and the finiteness or infinity of the 渭 Mm-D- orthogonal exponential system plays an important role in the study of whether the self-imitating measure is a spectral measure. Therefore, in this paper, the existence conditions and spectral properties of infinite orthogonal exponential function system under the space self-imitating measure are analyzed, and the following results are obtained: in the first part, By using the properties of the nonzero intermediate points in the set Z (MD) of zero points in the set of (x) zeros of functions (that is, points with coordinates of 0 or 1 / 2), many conditions are obtained for the existence of infinite 渭 Mm-D- orthogonal exponential functions under the space self-imitating measure. It lays a foundation for the further study of the spectral properties of the space self-imitating measure 渭 MfD. At the same time, some applications of these conclusions are given. 绗簩閮ㄥ垎,涓昏瀵逛笁缁寸┖闂碦3涓綋M=1/2[p1 p2,p1-p3,p2-p3; p1-p2,p1 p3,-p2 p3;-p1 p2,-p1 p3,p2 p3],D={0,e1,e2,e3}鏃，
本文编号：2126588
[Abstract]:The spectral and non-spectral problems of the self-imitating measure 渭 Mn-D are one of the main contents in the study of the spectrum theory of the self-imitating measure, and the finiteness or infinity of the 渭 Mm-D- orthogonal exponential system plays an important role in the study of whether the self-imitating measure is a spectral measure. Therefore, in this paper, the existence conditions and spectral properties of infinite orthogonal exponential function system under the space self-imitating measure are analyzed, and the following results are obtained: in the first part, By using the properties of the nonzero intermediate points in the set Z (MD) of zero points in the set of (x) zeros of functions (that is, points with coordinates of 0 or 1 / 2), many conditions are obtained for the existence of infinite 渭 Mm-D- orthogonal exponential functions under the space self-imitating measure. It lays a foundation for the further study of the spectral properties of the space self-imitating measure 渭 MfD. At the same time, some applications of these conclusions are given. 绗簩閮ㄥ垎,涓昏瀵逛笁缁寸┖闂碦3涓綋M=1/2[p1 p2,p1-p3,p2-p3; p1-p2,p1 p3,-p2 p3;-p1 p2,-p1 p3,p2 p3],D={0,e1,e2,e3}鏃，
本文编号：2126588
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