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We study a complex perturbation of a self-adjoint infinite band Schrodinger operator (defined in the form sense), and obtain the Lieb--Thirring type inequalities for the rate of convergence of the discrete spectrum of the perturbed operator to the joint essential spectrum of both operators.
The compression of the resolvent of a non-self-adjoint Schrodinger operator $-Delta+V$ onto a subdomain $Omegasubsetmathbb R^n$ is expressed in a Krein-Naimark type formula, where the Dirichlet realization on $Omega$, the Dirichlet-to-Neumann maps, a
We study perturbations of the self-adjoint periodic Sturm--Liouville operator [ A_0 = frac{1}{r_0}left(-frac{mathrm d}{mathrm dx} p_0 frac{mathrm d}{mathrm dx} + q_0right) ] and conclude under $L^1$-assumptions on the differences of the coefficient
Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral properties
In this article we consider asymptotics for the spectral function of Schrodinger operators on the real line. Let $P:L^2(mathbb{R})to L^2(mathbb{R})$ have the form $$ P:=-tfrac{d^2}{dx^2}+W, $$ where $W$ is a self-adjoint first order differential oper
We consider a Schrodinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half-line. We determi