与Grushin算子联系的标准正交小波基

Orthonormal wavelet bases adjusting to Grushin operator

通过对R2上与Grushin算子联系的拟距离,构造齐次型空间上的正交小波分解.这些小波的支集是拟距离意义下的二进制正方形,对其进行研究,得到R2中的一种多分辨率分析.

In this paper,orthonormal wavelets bases for the Grushin operator on R2 adapted to the quasi-distance are constructed.The supports of these wavelets are binary squares in the sense of a quasi-distance and a new“multiscale analysis”type in R2 is given after comparison with the classical ones.