A construction of multiscale bases for Petrov–Galerkin methods for integral equations

In this paper, a construction of multiscale bases for Petrov–Galerkin methods for Fredholm integral equations of the second kind is proposed. The properties of multiscale bases are presented including additional order of vanishing moments, compact supports and stability. Communicated by A. Zhou Dedicated to Professor Charles A. Micchelli on the occasion of his sixtieth birthday with friendship and esteem Mathematics subject classifications (2000) 41A10, 65R20, 65D15. Min Huang: Supported in part by Professor Yuesheng Xu's support under the program of “One Hundred Distinguished Young Scientists” of the Chinese Academy of Sciences and by the Graduate Innovation Foundation of the Chinese Academy of Sciences.