Spectral theory of operators
Research on spectral operator theory covers the problems of spectral stability of differential operators associated with boundary value problems in varying the domain of their definition, as well as the problems of convergence and summability of spectral expansions by eigenfunctions of differential operators, such as the Laplace operator in the multidimensional domain.
The goal of these studies is to obtain accurate characteristics of the variation of the field, providing a robust evaluation of the variance of eigenvalues of differential operators.
The results obtained will be used in the construction of the general theory of spectral stability of differential operators on certain classes of Lipschitz regions, in the construction of expansions of the eigenfunctions of differential operators and in the construction of solutions to boundary value problems using the Fourier method.