LOCAL WAVELET TRANSFORM ON THE SMOOTH SURFACE OF ROTATION CLASS

摘要

For the smooth surface of rotation class M, the explicit construction of two local flattening maps p are given. By virtue of the inverse projection p~(-1), where the bijection projection p is the local flattening map from a two-dimensional smooth surface M of rotation class to a plane, the local wavelet transform on M can be generated from wavelet transform on a plane. For the two examples of the quadratic parameter rotation surface and parabolic general rotation surface, by using the two local flattening maps p respectively, the construction of the local dilation is systematically studied, and local wavelet transform of them is offered. We also show the local wavelet graphical representation on the quadratic parameter rotation surface and parabolic general rotation surface. Finally, the inverse transform formula of the local wavelet transform, that is, the reconstruction formula is also offered.