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On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

Zagorodniuk, S. (1998)

Serdica Mathematical Journal

∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an important role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis. It is known, that classical polynomials have a number of properties, which uniquely define them.

On discreteness of spectrum of a functional differential operator

Sergey Labovskiy, Mário Frengue Getimane (2014)

Mathematica Bohemica

We study conditions of discreteness of spectrum of the functional-differential operator $ℒ u = - u^{''} + p (x) u (x) + \int_{- \infty}^{\infty} (u (x) - u (s)) d_{s} r (x, s)$ on $(- \infty, \infty)$ . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

Displaying 1 – 13 of 13

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

On discreteness of spectrum of a functional differential operator

On Floquet eigenvalue problems for first order differential systems in the complex domain.

On nonresonance problems of second-order difference systems.

On rational and periodic solutions of stationary KdV equations.

On sampling expansions of Kramer type.

On the differential operators with periodic matrix coefficients.

On the periodic spectrum of the 1-dimensional Schrödinger operator.

On the singular spectrum of discrete Schrödinger operator

On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces.

On the spectrum of a discrete non-Hermitian quantum system.

Optimization of the principal eigenvalue of the one-dimensional Schrödinger operator.

Oscillation theory for a pair of second order dynamic equations with a singular interface.

Currently displaying 1 – 13 of 13