Multiple fourier series and integrals

Abstract

One gives a brief survey of the investigations on the theory of multiple Fourier series and integrals, reviewed in Referativnyi Zhurnal “Matematika” in the period 1953–1980. Principal attention is given to the following questions: localization principles, uniform convergence and summability, convergence and summability at a point, in the Lp metric, and almost everywhere, absolute convergence, uniqueness theorems, conjugate Fourier series and integrals, equiconvergence and equisummability of Fourier series and integrals, properties of the kernel and of the Lebesgue constant of summation methods of Fourier series, Fourier coefficients and Fourier transforms.