一类自仿测度下的正交指数函数的个数

The Cardinality of Orthogonal Exponential Functions Under a Class of Self-affine Measures

分形测度的谱或非谱问题是调和分析中最活跃的研究领域之一,某些分形Hilbert空间中存在无穷多个指数函数系,使得构成一个标准正交基.这个时候该测度称为谱测度.为此,讨论了一类Bernoulli卷积测度下的正交指数函数的个数.

The spectrality or non-spectrality of fractal measures is one of the active research area of the Harmonic analysis. Some of the fractal Hilbert spaces admit infinitely many orthogonal exponential function systems such that composite an orthonormal basis.At this time we call this measure is a spectral measure. In this paper we discuss the cardinality of orthogonal exponential functions under a class of Bernoulli convolution measures.