Representation of differential operators in wavelet basis
The paper under review provides a formula for matrix representations of general partial differential operators of the form \(g(\partial_x, \partial_y)\), where \(g\) is an arbitrary analytic function of two variables. The representations are done with respect to two-dimensional periodic orthonormal wavelet bases. In this sense, the paper generalizes the work of \textit{G. Beylkin} [SIAM J. Numer. Anal. 29, No. 6, 1716--1740 (1992; Zbl 0766.65007)].
scientific article; zbMATH DE number 2142364
scientific article