НЕОБХОДИМЫЕ УСЛОВИЯ СУММИРУЕМОСТИ СПЕКТРАЛЬНЫХ РАЗЛОЖЕНИЙ, СВЯЗАННЫХ С ЭЛЛИПТИЧЕСКИМИ ОПЕРАТОРАМИ

Аннотация

Subjects of inquiry: objects of research arc spectral decomposition and their Riesz means of the functions describing various physical processes. Aim of the inquiry: necessary conditions of summability of the spectral decomposition connected with various elliptic operators. Methods of inquiry: modem methods of the theory of functions, the functional analysis, the spectral theory of operators arc applied. The results achieved and their novelty: all results arc new: 1) necessary conditions of convergence of Riesz means of spectral decomposition on eigenfunctions of operator Laplace arc established. 2) necessary conditions of convergence of spectral decomposition on eigenfunctions of polyharmonic operators arc found. 3) the conditions of the generalized continuity necessary for summability of spectral decomposition on eigenfunctions of Schrodinger operator in an arbitrary three-dimensional domain are received. 4) necessary conditions of convergence of spectral decomposition of functions from Sobolev space by eigenfunctions of Laplas-Bcltrami operator arc found. Practical value: dissertation’s results are theoretical. Degree of embed and economic efficiency: on the basis of received results a special course will be read for the students of the magistracy. Sphere of usage: results and the methods presented in work can be used in scientific researches in mathematical physics, mathematical analysis and functional analysis.