微分方程和连续小波变换

Differential equation and continuous wavelet transform

利用连续小波变换讨论了微分方程和积分方程之间的关系 ,并得到了一类微分方程利用连续小波变换能够变换成等价的积分方程的结果 .它们不仅在弱收敛意义下是等价的 ,而且在范数收敛意义下是等价的 ,从而将微分方程的讨论与积分方程的讨论联系起来 ,使得连续小波变换能够在讨论微分方程和积分方程的过程中得到应用 .

We discuss the relation between differential equations and integral equations by using the continuous wavelet transform, showing that some differential equations can be transformed into the integral equations by using the continuous wavelet transform. They are equivalent not only in the sense of weak convergence but also in the sense of norm convergence. Associating the discussion of the differential equations with the discussion of the integral equation makes continuous wavelet transform be applied into the discussion of the differential equations and the integral equations.