Pointwise Convergence of a Class of Multi-dimensional Continuous Wavelet Inverse Transform

In this work, a pointwise convergence of multi-dimensional continuous wavelet inverse transform was studied. Firstly, a kind of multi-dimensional continuous wavelet transform was introduced, which features small shift at high frequency and large shift at low frequency. Secondly, the pointwise converfence of muti-dimensional continuous wavelet was discussed, and a sufficient condition for the pointwise convergence of this multi-dimensional continuous wavelet inverse transform was given.