Related papers: The characterization problem for one class of seco…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
We consider a quadratic operator pencil with a small periodic perturbation multiplied by the spectral parameter. It is motivated, in particular, by a one-dimensional Klein-Gordon equation with a time-parity-symmetric perturbation. We study…
This paper is concerned with the reduction of the spectral problem for symmetric linear operator pencils to a spectral problem for the single operator. Also, a Rayleigh-Ritz-like bounds on eigenvalues of linear operator pencils are…
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
In this paper, partial inverse problems for the quadratic pencil of Sturm-Liouville operators on a graph with a loop were studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the $s$th power of a positive definite operator having a discrete spectrum in…
The question of defining unique, generally applicable constrained second, and higher-order, derivatives is investigated. It is shown that second-order constrained derivatives obtained via two successive constrained differentiations provide…
We will show a local solvability result for a class of degenerate second order linear partial differential operators with a complex subprincipal symbol. Due to the form of the operators in the class the subprincipal symbol is invariantly…
Any traditional classification problem in general involves modelling individual classes and in turn classification by evaluating the similarity of the test set with the modelled classes. In this paper, we introduce another approach that…
We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in Schauder spaces by…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
The explicit connection between the transition matrix and boundary element method integral operators is formulated. This enables the calculation of characteristic modes via eigenvalue problems involving either set of operators, leading to…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence…