Given an infinite graph $G$ on countably many vertices, and a closed, infinite set $Λ$ of real numbers, we prove the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $Λ$.
First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral data.
In this paper we present new L-borderenergetic graphs, this is, graphs which are L-noncospectral with Kn but have the same Laplacian energy. We also present some graphs which are noncospectral to respective normalized Laplacian energy and they have the same normalized Laplacian energy.
In this article we prove results on logaritmic convexity of fixed points of stochastic kernel operators. These results are expected to play a key role in the economic application to strategic market games.
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators $L_{t}(q)$ with $q\in L^{1}[0,1]$ and quasi-periodic boundary conditions, $t\in [0,2π)$, when there is not any additional condition on the potential $q$.
In this paper, we consider the nonselfadjoint Sturm Liouville operator with and either periodic, or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis in in terms of the Fourier coefficients of q.
The multiplicity of the lowest eigenvalue E of the so-called non-commutative harmonic oscillator Q(α,β) is studied. It is shown that E is simple for αand βin some region.
We discuss resonances for 1D massless Dirac operators with compactly supported potentials on the line. We estimate the sum of the negative power of all resonances in terms of the norm of the potential and the diameter of its support.
In this paper we use the matrix analogue of eigenvalue $ρ_{min}^{2}$ to formulate and to solve the extremal Nehary problem. When $ρ_{min}$ is a scalar, our approach coincides with Adamjan-Arov-Krein approach.
We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.
The Sturm--Liouville problem $-y''-λρy=0$, $y(0)=y(1)=0$, where $ρ$ is a generalized derivative of self-similar function $P\in L_2[0,1]$ with spectral degree D=0, is studied. Asymptotic formulas for eigenvalues are obtained.
We discuss applications of the M. G. Kreĭn theory of the spectral shift function to the multi-dimensional Schrödinger operator as well as specific properties of this function, for example, its high-energy asymptotics. Trace identities for the Schrödinger operator are derived.
We confirm rigorously the conjecture, based on numerical and asymptotic evidence, that all the eigenvalues of a certain non-self-adjoint operator are real.
There have been several recent papers on the subject of the P-hull and the SP-hull of an l-group (lattice-ordered group). The most natural formulation of the concepts was given by P. Conrad in [6]. T. Speed studied P-groups extensively in [11]; his work was motivated by earlier work by H. Nakano and I. Amemiya in a vector lattice setting. A. Vecksler [12] produced the SP-hull for f-rings. The ortho-completion of S. Bernau [2] is a related concept.
We present a point of view on results of the paper of Geronimo and Johnson [Comm. Math, Phys. 193 (1998)] that allow infinitely dimensional generalization up to the case when spectrum is supported on a Cantor set of positive Lebesgue measure.