一类四元素数字集的正交函数的个数

周脉东

(1.陕西师范大学数学与信息科学学院,陕西 西安 710062;2.陕西教育学院数学系,陕西 西安 710061)

一类四元素数字集的正交函数的个数

周脉东1,2

(1.陕西师范大学数学与信息科学学院,陕西 西安 710062;2.陕西教育学院数学系,陕西 西安 710061)

自仿测度的谱与非谱问题近年引起了很大的关注,关于自仿测度的非谱问题,其中之一就是要估算它在L2空间上的正交指数的个数.通过对µM,D傅里叶变换的零点集性质的分析和讨论,对现有的结论进行了改进,确定了相应四元素数字集的平面自仿测度在L2的空间上正交指数函数的最大个数为3.

自仿测度;谱测度;正交指数函数;迭代函数系

1 引言

关于非谱测度µM,D,在L2(µM,D)上存在至多有限个正交指数,主要的问题是证明在L2(µM,D)上正交指数的个数并找出它们来.文献 [3]证明了在广义平面 Sierpinski垫在 L2(µM,D)上的正交指数的个数最多是3个,文献[4-5]在此基础上给出了更一般的结论.文献[6] (定理2)对于给出的扩张矩阵和四个元素的数字集,证明了最多存在4个相互正交的指数函数,本文改进了文献[6]中定理2的结论,证明了相互正交的指数函数最多为3个.

2 定理及证明

3 结论

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[3] Li Jianlin. Orthogonal exponential on the generalized plane Sierpinski gasket[J].J.Approx Theory, 2008,153(2):161-169.

[4]Li Jianlin.Non-spectral problem for a class of planar self-affine measure[J].J.Funt.Anal.,2008,255(11)11: 3125-3148.

[5]Li Jianlin.Non-spectrality of planar self-affine measure with three-element digit set[J].J.Funt.Anal., 2009,257(2):537-552.

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The cardinality of a class of orthogonal exponential function with four-element digit set

Zhou Maidong1,2
(1.College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China;
2.Department of Mathematics,Shaanxi Institute of Education,Xi′an 710061,China)

The problem of the spectrality or non-spectrality of a self-affine measure have been

much attention in recent years.One of non-spectrality problem on a self-affine measure is to estimate the number of orthogonal exponentials in L2.By the analysis of characterization of the zero set of the Fourier transform of µM,D,Improve the result and get the biggest number of the orthogonal exponential functions of planar self-affine measure with four-elements digit set for the L2space is 3.

self-affine measure,spectral measure,orthogonal exponential functions,iterated function system

O174.12

A

1008-5513(2012)01-0080-05

2011-02-10.

陕西省科学技术研究发展计划（二）项目(2011JE002).

周脉东(1969-),硕士,讲师,研究方向：谱测度及其理论.

2010 MSC:42B10