A local wavelet transform on the torus T-2

摘要

For the smooth surface M, the explicit construction of local flattening map p is given, where the bijection projection p is the local flattening map from a smooth surface M to a plane. By virtue of the inverse projection p(-1), the local wavelet transform on M can be generated from wavelet transform on a plane. Take the torus T-2 for example, by using the local flattening map p of torus, the construction of the local dilation on the torus is systematically studied, the local wavelet transform formula on the torus is offered and the inverse transform formula of the local wavelet transform, that is, the reconstruction formula is also offered. Finally, we show the graphical representation of the local wavelet on the torus.