Shota Rustaveli National Science Foundation of GeorgiaStart Date: 2018-12-13 End Date: 2021-12-12
The project proposal is dedicated to the study of modern topics in the theory of integral operators in non-standard function spaces, weight theory of integral operators, multidimensional Fourier Analysis and Applied Harmonic Analysis, applications to partial differential equations (PDEs). In particular, it is proposed:to solve the coefficients reconstruction problem for convergent multiple function series in general case via the introduction of so called Cantor’s trigonometric integral; to solve the representability problem for real valued continuous function of several variables by the series of functions of single (generally speaking) different variables. We plan to extend Sierpinski’s theorem which is well-known for one-dimensional case. We emphasize the deep investigation of convergence (resp. divergence) problems for multiple Fourier series. Namely, the behavior of “spherical” terms of divergent double Fourier Walsh-Paley series of functions from L^p (1