【摘要】：自仿測度μM,D的譜與非譜問題是自仿測度譜理論研究的主要內容之一而μM,D-正交指數(shù)系的有限性或無限性問題在研究自仿測度是否為譜測度中起著重要的作用.因此,本文主要針對空間自仿測度下無限正交指數(shù)函數(shù)系存在的條件及譜性質進行分析,得到如下研究結果：第一部分,通過利用函數(shù)mD(x)零點集Z(mD)中的非零中間點(即坐標為0或1/2的點)的性質,得到空間自仿測度下無限μM,D-正交指數(shù)函數(shù)系存在的許多條件,為進一步研究空間自仿測度μM,D的譜性質奠定基礎.同時,給出這些結論的一些應用.第二部分,主要對三維空間R3中當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}時,其中pj∈Z\{0,±1}(j=1,2,3),e1,e2,e3是R3中的單位向量,自仿測度μM,D的譜性質進行分析,得到的結果是(1)當pj∈2Z\{0,2}(j=1,2,3)或p1=p2=p3=2時,μM.D是譜測度；(2)當p1,p2,p3這三個數(shù)中至少有一個數(shù)是偶數(shù)時,空間L2(μM,D)中存在無限正交系E(A)且A(?)Z3；(3)當pj∈2Z+1\(±1}(j=1,2,3)時,PM,D不是譜測度,且空間L2(μM,D)中正交指數(shù)函數(shù)系至多包含“4”個元素,且數(shù)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. 絎簩閮ㄥ垎,涓昏瀵逛笁緇寸┖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，

本文編號：2126588