连续小波变换在多元函数空间中的应用

An application of the continuous wavelet transform in multivariate function space

使用连续小波变换讨论了某些偏微分方程和相应的积分方程之间的关系.使用连续小波变换能够将这些偏微分方程变换成相应的积分方程,这些偏微分方程与相应的积分方程不仅在弱收敛意义下是等价的,而且在范数收敛意义下也是等价的.

The relation between the partial differential equations and the integral equations are discussed by using the continuous wavelet transform. The result that the partial differential equations can be transformed into the integral equations is obtained and they are equivalent not only in weak topology but also in strong topology.