spectrum.

Generalization of Method A. A. Dorodnicyn Close Calculation of Eigenvalues and Eigenvectors of Symmetric Matrices on Case of Self-Conjugate Discrete Operators

Authors: Maleko Е. М.

Let the discrete self-conjugate operator A operates in separable Hilbert space H and has the kernel resolvent with simple spectrum. Self-conjugate and limited operator B operates also in H. Then it is possible to find such number ε > 0, that eigenvalues and eigenfunctions of the perturbation operatorA+εB will be calculated on a method of Dorodnicyn.

About reversibility states of linear differential operators with periodic unbounded operator coefficients

Authors: Didenko V. B.

For investigated linear differential operator (equation) with unbounded periodic operator coefficients defined at one of the Banach space of vector functions defined on all real axis difference operator (equation) with constant operator coefficient defined at appropriate Banach space of two-side vector sequences is considered. For differential and difference operators propositions about kernel and co-image dimensions coincidence, simultaneous complementarity of kernels and images, simultaneous reversibility, spectrum interrelation are proved.