On the restoration of an operator of Sturm-Liouville by one spectrum

On the Spectral Properties of a Wave Operator Perturbed by a Lower-Order Term

“…The eigenfunctions constructed in this paper coincide with the eigenfunctions constructed earlier in the work of R.A. Aleksandaryan [9]. In this paper, the spectral properties of a beam of operators with a wave operator in the principal part were studied by the methods of [16]- [21].…”

“…Note that the operator (13)-(14) is a two-dimensional generalization of the operator discussed in [16] - [17], which has found application to singularly perturbed Cauchy problem [18], to the operator of the heat conductivity in [19], and to the ill-posed problems of mathematical physics in [20] - [21], and Volterra problems in [26] - [27].…”

On Projectional Orthogonal Basis of a Linear Non-Self -Adjoint Operator

“…Moreover, 0, 1 sin 2 , which confirms results of the main Theorem 3.1. We note that Sturm-Liouville operators of the class, that we studied, are reconstructed in a single spectrum [34].…”

ABOUT SINGLE OPERATOR METHOD OF SOLUTION OF A SINGULARLY PERTURBED CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION n – ORDER

“…With the help of direct calculations, the generality of the obtained recurrent formula is shown, and additional conditions that appeared in the course of research are removed. This work completes a series of studies devoted to the development of a spectral method for solving ill-posed problems [17][18][19][20][21][22][23][24][25].…”