中文摘要：

针对分数阶傅立叶变换在工程技术上的广泛应用,引入分数阶傅立叶变换与分数阶多尺度多分辨分析的概念.运用时频分析与泛函分析、分数阶傅立叶变换,研究了分数阶多分辨分析的构造方法,刻画了分数阶多尺度多分辨分析的特征.给出了分数阶多重尺度函数的存在条件.

英文摘要：

Aimed at widespread application of fractional Fourier transform in engineering and technology, the concepts of fractional Fourier transform and fractional multidiemension-multi-resolution analysis are introduced in this article. The methods for construction of fractional multiresolution analysis are investigated with time-frequency analysis, functional analysis, and fractional Fourier transform： The fractional multidimension-multiresolution analysis is characterized, also. The existence conditions of the fractional multidimensional function are given out at the end.