纯粹数学与应用数学
純粹數學與應用數學
순수수학여응용수학
PURE AND APPLIED MATHEMATICS
2012年
1期
80-84
,共5页
自仿测度%谱测度%正交指数函数%迭代函数系
自倣測度%譜測度%正交指數函數%迭代函數繫
자방측도%보측도%정교지수함수%질대함수계
self-affine measure%spectral measure%orthogonal exponential functions%iterated function system
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．
自倣測度的譜與非譜問題近年引起瞭很大的關註，關于自倣測度的非譜問題，其中之一就是要估算它在L2空間上的正交指數的箇數．通過對μM，D傅裏葉變換的零點集性質的分析和討論，對現有的結論進行瞭改進，確定瞭相應四元素數字集的平麵自倣測度在L2的空間上正交指數函數的最大箇數為3．
자방측도적보여비보문제근년인기료흔대적관주，관우자방측도적비보문제，기중지일취시요고산타재L2공간상적정교지수적개수．통과대μM，D부리협변환적영점집성질적분석화토론，대현유적결론진행료개진，학정료상응사원소수자집적평면자방측도재L2적공간상정교지수함수적최대개수위3．
The problem of the spectrality or non-spectrality of a self-affine measure have been received much attention in recent years. One of non-spectrality problem on a self-affine measure is to estimate the number of orthogonal exponentials in Lu. 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 L2 space is 3.
