We study the spectral problem for the Dirac operator with degenerate boundary conditions and a complex-valued summable potential. Sufficient conditions are found under which the spectrum of the problem under consideration coincides with the spectrum of the corresponding unperturbed operator.
This paper is deals with the concept of weakly (Λ, sp)-continuous multifunctions. In particular, some characterizations of weakly (Λ, sp)-continuous multifunctions are investigated.
We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.
In this article we obtain asymptotic formulas for the Bloch eigenvalues of the operator generated by a system of Schrodinger equations with periodic PT-symmetric complex-valued coefficients. Then using these formulas we classify the spectrum of this operator and find a condition on the coefficients for which the spectrum contains a half line.
In this expository work, we collect some background results and give a short proof of the following theorem: periodic Jacobi matrices on $\mathbb{Z}^d$ exhibit strong ballistic motion.
In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on ${\Z}^d$ for \textit{arbitrary} $d\geq1$.
We examine semiclassical magnetic Schrödinger operators with complex electric potentials. Under suitable conditions on the magnetic and electric potentials, we prove a resolvent estimate for spectral parameters in an unbounded parabolic neighborhood of the imaginary axis.
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
It is shown that transfer functions, which play a crucial role in M.G. Krein's study of inverse spectral problems, are a proper tool to formulate local spectral uniqueness conditions.
Our main result is an elementary derivation of the spectral decomposition of hypermatrices generated by arbitrary combinations of Kronecker products and direct sums of cubic side length 2
We prove the completeness of the generalized (interior) transmission eigenstates for the acoustic and Schrödinger equations. The method uses the ellipticity theory of Agranovich and Vishik.
This paper is on magnetic Schrodinger operators in two dimensional domains with corners. Semiclassical formulas are obtained for the sum and number of eigenvalues. The obtained results extend former formulas for smooth domains in \cite{Fr, FK} to piecewise smooth domains.
We consider spectral problems for the Sturm-Liouville operator with arbitrary complex-valued potential q(x) and degenerate boundary conditions. We solve corresponding inverse problem, and also study the completeness property and the basis property of the root function system.
Sturm-Liouville spectral problem for equation $-(y'/r)'+qy=λpy$ with generalized functions $r\ge 0$, $q$ and $p$ is considered. It is shown that the problem may be reduced to analogous problem with $r\equiv 1$. The case of $q=0$ and self-similar $r$ and $p$ is considered as an example.
For a geometrically finite hyperbolic surface of infinite volume we write down the spectral decomposition for the Laplacian on 1-forms, generalize the Kudla and Millson's construction of hyperbolic Eisenstein series and other related results.
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
By approximation, I show that the spectrum of the Schrödinger operator with potential $V(n) = f(nρ\pmod 1)$ for f continuous and $ρ> 0$, $ρ\notin \N$ is an interval.
We prove that some perturbation of a J-selfadjoint second order differential operator admits factorization and use this new representation of the operator to prove compactness of its resolvent and to find its domain.