Mean-Periodicity in Several Variables

摘要

The author concentrated on extending this theory of mean-periodicity for functions of one variable to functions of several variables. The purpose is to obtain a representation of solution of homogeneous convolution equations through a sum or integral of exponential functions, a sort of extension of the notion of Fourier series. This problem of spectral synthesis, which forms the core of our investigations, is so formulated as to depend upon a sufficiently concrete characterisation Q of a certain quotient space. This problem of characterisation then amounts to proving that a correspondence rho is an isomorphism. But proving the injectivity and surjectivity of rho constitute two exceedingly interesting and far-reaching problems of complex analysis. (Author)