Related papers: Resonances and Spectral Shift Function near the La…

We consider decaying oscillatory perturbations of periodic Schr\"odinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variation condition at infinity and an $L^p$ decay condition. We…

We consider a Schr\"odinger Operator with a matrix potential defined in $L_2^m(F)$ by the differential expression\begin{equation*} L(\phi(x))=(-\Delta+V(x))\phi(x) \end{equation*}and the Neumann boundary condition, where $F$ is the $d$…

We prove that Schr\"odinger operators with meromorphic potentials $(H_{\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+ \frac{g(\theta+n\alpha)}{f(\theta+n\alpha)} u_n$ have purely singular continuous spectrum on the set $\{E:…

We consider a Schr\"odinger operator $H=-\Delta+V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized…

We investigate the amplitude (Higgs) mode of the relativistic O(N) model in the vicinity of the Wilson-Fisher quantum critical point in D=4-epsilon spacetime dimensions. We compute the universal part of the scalar spectral function near the…

In the paper we consider a functional-difference operator $H=U+U^{-1}+V$, where $U$ and $V$ are self-adjoint Weyl operators satisfying $UV=q^{2}VU$ with $q=e^{\pi i\tau}$ and $\tau>0$. The operator $H$ has applications in the conformal…

In this paper, we consider the Schr\"odinger equation, \begin{equation*} Hu=-u^{\prime\prime}+(V(x)+V_0(x))u=Eu, \end{equation*} where $V_0(x)$ is 1-periodic and $V (x)$ is a decaying perturbation. By Floquet theory, the spectrum of…

We characterize the Hermite-Biehler (de Branges) functions $E$ which correspond to Shroedinger operators with $L^2$ potential on the finite interval. From this characterization one can easily deduce a recent theorem by Horvath. We also…

We consider a semiclassical $2\times 2$ matrix Schr\"odinger operator of the form $P=-h^2\Delta {\bf I}_2 + {\rm diag}(V_1(x), V_2(x)) +hR(x,hD_x)$, where $V_1, V_2$ are real-analytic, $V_2$ admits a non degenerate minimum at 0, $V_1$ is…

In this note, we prove weighted resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at…

We prove Strichartz estimates for the Schroedinger operator $H = -\Delta + V(t,x)$ with time-periodic complex potentials $V$ belonging to the scaling-critical space $L^{n/2}_x L^\infty_t$ in dimensions $n \ge 3$. This is done directly from…

The goal of this paper is the spectral analysis of the Schr\"{o}dinger operator $H=L+V$ , the perturbation of the Taibleson-Vladimirov multiplier $L=\mathcal{D}^{\alpha}$ by a potential $V$. Assuming that $V$ belonges to a class of fast…

We consider the semiclassical Schr\"odinger operator $-h^2\partial_x^2+V(x)$ on a half-line, where $V$ is a compactly supported potential which is positive near the endpoint of its support. We prove that the eigenvalues and the purely…

We consider the discrete one-dimensional Schr\"{o}dinger operator $H=H_0+V$, where $(H_0x)[n]=-(x[n+1]+x[n-1]-2x[n])$ and $V$ is a self-adjoint operator on $\ell^2(\mathbb{Z})$ with a decay property given by $V$ extending to a compact…

We study the spectral problems associated with the finite-difference operators $H_N = 2 \cosh(p) + V_N(x)$, where $V_N(x)$ is an arbitrary polynomial potential of degree $N$. These systems can be regarded as a solvable deformation of the…

For a one-dimensional discrete Schr\"odinger operator with a weakly coupled potential given by a strongly mixing dynamical system with power law decay of correlations, we derive for all energies including the band edges and the band center…

The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including properties of functions of completely…

We study the eigenvalues of the magnetic Schroedinger operator associated with a magnetic potential A and a scalar potential q, on a compact Riemannian manifold M, with Neumann boundary conditions if the boundary is not empty. We obtain…

Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by…

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant H\"older…