Related papers: On non-selfadjoint operators with finite discrete …

We investigate the spectral properties of self-adjoint Schr\"odinger operators with attractive $\delta$-interactions of constant strength $\alpha > 0$ supported on conical surfaces in ${\mathbb R}^3$. It is shown that the essential spectrum…

We analyze the perturbations $T+B$ of a selfadjoint operator $T$ in a Hilbert space $H$ with discrete spectrum $\{t_k \}$, $T \phi_k = t_k \phi_k$, as an extension of our constructions in arXiv: 0912.2722 where $T$ was a harmonic oscillator…

Let $H := H_{0} + V$ and $H_{\perp} := H_{0,\perp} + V$ be respectively perturbations of the free Schr\"odinger operators $H_{0}$ on $L^{2}\big(\mathbb{R}^{2d+1}\big)$ and $H_{0,\perp}$ on $L^{2}\big(\mathbb{R}^{2d}\big)$, $d \geq 1$ with…

We give a family of examples of discrete Schr\"odinger operators whose spectral dimension is not invariant under sieving. The examples are produced from the Fibonacci Hamiltonian, which is one of the main models of a one-dimensional…

We investigate the spectral properties of the Schr\"odinger operators in $L^2(\mathbb{R}^n)$ with a singular interaction supported by an infinite family of concentric spheres $$…

We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…

This paper is devoted to the definition and analysis of the spectral shift function (SSF) associated with non-self-adjoint perturbations of self-adjoint operators. Motivated by applications in scattering theory, we consider both trace-class…

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index…

This paper is devoted to self-adjoint cyclically compact operators on Hilbert--Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators are given. We apply this result to partial…

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain…

This is a sequel of a recent article by Borichev-Golinskii-Kupin, where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk which satisfy certain growth hypotheses. These results were…

In this paper, we give Lieb-Thirring type inequalities for isolated eigenvalues of $d$-dimensional non-selfadjoint Schr\"{o}dinger operators with complex-valued and dilation analytic potentials. In order to derive them, we prove that…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded semidefinite perturbation is considered. A variant of the Davis-Kahan $ \sin2\Theta $ theorem from [SIAM J. Numer. Anal. 7 (1970), 1--46]…

We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…

We consider the scattering theory for discrete Schr\"odinger operators on $Z^d$ with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus…

This is a continuation of our papers \cite{AP2} and \cite{AP3}. In those papers we obtained estimates for finite differences $(\D_Kf)(A)=f(A+K)-f(A)$ of the order 1 and $(\D_K^mf)(A)\df\sum\limits_{j=0}^m(-1)^{m-j}(m\j)f\big(A+jK\big)$ of…

We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle. Despite its model and rather abstract character this question is worth…

We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…

Given a self-adjoint operator $T$ on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set $\mathcal D(T)$ of all possible diagonals of $T$. For operators $T$ with at least two points in their…

We obtain bounds on the complex eigenvalues of non-self-adjoint Schr\"odinger operators with complex potentials, and also on the complex resonances of self-adjoint Schr\"odinger operators. Our bounds are compared with numerical results, and…