In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued coefficients, under which the operator is a spectral operator in the sense of Dunford [1].
In this paper, we consider the band functions, Bloch functions and spectrum of the self-adjoint differential operator L with periodic matrix coefficients. Conditions are found for the coefficients under which the number of gaps in the spectrum of the operator L is finite
In this paper we investigate the spectrum of the Dirac operator posed in a tubular neighborhood of a planar loop with infinite mass boundary conditions. We show that when thewidth of the tubular neighborhood goes to zero the asymptotic expansion of the eigenvalues isdriven by a one dimensional operator of geometric nature involving the curvature of the loop.
The main result proved in [The eigenvalues of a tridiagonal matrix in biogeography, Appl. Math. Comput. 218 (2011) 195-201; MR2821464] by B. Igelnik and D. Simon is virtually the Sylvester determinant.
We study the spatial asymptotics of Green's function for the 1d Schrodinger operator with operator-valued decaying potential. The bounds on the entropy of the spectral measures are obtained. They are used to establish the presence of a.c. spectrum
In this paper, a diffusion operator including conformable fractional derivatives of order α (α in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained. Furthermore, an effective procedure for solving the inverse nodal problem is given.
We prove the Cesàro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in particular, on the continuous version of a theorem by A. Mate, P. Nevai and V. Totik from 1991.
Our goal in this paper is to find an estimate for the spectral gap of the Laplacian on a 2-simplicial complex consisting on a triangulation of a complete graph. An upper estimate is given by generalizing the Cheeger constant. The lower estimate is obtained from the first non-zero eigenvalue of the discrete Laplacian acting on the functions of certain sub-graphs.
The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2π), x'(0) = x'(2π)$ and $x''(0) = x''(2π)$. Our approach is based on the R-boundedness and $L^{p}$-multiplier of linear operators.
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.
In this paper we investigate the spectrum and spectrality of the one-dimensional Schrodinger operator with a periodic PT-symmetric complex-valued potential.
We establish equality between the essential spectrum of the Schroedinger operator with magnetic field in the exterior of a compact arbitrary dimensional domain and that of the operator defined in all the space, and discuss applications of this equality.
We analyze the spectra of generalized Fibonacci and Fibonacci-like operators in Banach space $l^1$. Some of the results have application in population dynamics.
In this note we extend the necessary and sufficient conditions of Boyle-Handleman 1991 and Kim-Ormes-Roush 2000 for a nonzero eigenvalue multiset of primitive matrices over $\R_+$ and $\Z_+$, respectively, to irreducible matrices.
Using the spectral theory of weakly convergent sequences of finite graphs, we prove the uniform existence of the integrated density of states for a large class of infinite graphs.
In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.