Spectral behavior of matrix sequences and discretized boundary value problems

On Matrix Boundary Value Problems

Introduction. In a recent publication1 a matrix type of boundary value problem was introduced in order to simplify the description of nuclear reactions. It appeared that this type of boundary value problem could find applications in other branches of mathematical physics, and the purpose of the present note is to illustrate them. When we deal with vibrations of continuous media, with problems o...

Spectral Theory of Boundary Value Problems

‎Solving Some Initial-Boundary Value Problems Including Non-classical ‎C‎ases of Heat Equation By Spectral and Countour Integral ‎Methods‎

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

Spectral Estimation and Inverse Initial Boundary Value Problems

We extend the classical spectral estimation problem to the infinitedimensional case and propose a new approach to this problem using the Boundary Control (BC) method. Several applications to inverse problems for partial differential equations are provided.

Spectral Boundary Value Problems and their Linear Operators

The paper offers a self-consistent account of the spectral boundary value problems developed from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary condition is introduced and results on its solvability complemented by representations of weak and strong solutions are obtained. The question of ex...