Harmonic analysis in the Schwartz distribution spaces and some applications to nonclassical problems of mathematical physics
The author constructs a special tool of harmonic analysis in Schwartz distribution spaces which generalizes the main facts of harmonic analysis in \(L_2(\mathbb R^2)\) to the indicated spaces. By means of this apparatus, the structure of some distributions in \(Z'(\mathbb R^n)\) with nonalgebraic singularities at isolated points is described. An essential part of this article is an application of harmonic analysis in \(Z'(\mathbb R^n)\) to the solvability of some equations with constant coefficients. The necessity of this investigation stems from the fact that solutions to these equations may have nonalgebraic singularities at isolated points. The well-posedness of some nonclassical boundary value problems of mathematical physics is studied in this class.
scientific article; zbMATH DE number 1431660