Related papers: On Parseval frames of exponentially decaying compo…

Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\bigcup_{j\in J}\Delta_j$, $J\subseteq\mathbb{Z}$, of segments $\Delta_j=[\alpha_j,…

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a compact Lie group $G$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. Using Fourier integral operator…

The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…

We study the manner in which a sequence of spectral shift functions $\xi(\cdot;H_j,H_{0,j})$ associated with abstract pairs of self-adjoint operators $(H_j, H_{0,j})$ in Hilbert spaces $\cH_j$, $j\in\bbN$, converge to a limiting spectral…

Let $\gH$ be a Hilbert space and let $A$ be a simple symmetric operator in $\gH$ with equal deficiency indices $d:=n_\pm(A)<\infty$. We show that if, for all $\l$ in an open interval $I\subset\bR$, the dimension of defect subspaces…

Spectral components of one-dimensional Schr\"odinger operator with complex potential are investigated. An effective upper bound for the total number of eigenvalues and spectral singularities is established. For dissipative Schr\"odinger…

Let $(X,\omega_0):=(\mathbb{C}/\Lambda,0)$ denote the elliptic curve associated to the lattice $\Lambda$, $X_2:=\{\omega_0,\cdots, \omega_3\}$ its set of half-periods and $\wp:X \to \mathbb{P}^1$ the usual Weierstrass $\wp$ function, with a…

The paper studies the spectral properties of the Schr\"odinger operator $A_{gV} = A_0 + gV$ on a homogeneous rooted metric tree, with a decaying real-valued potential $V$ and a coupling constant $g\ge 0$. The spectrum of the free Laplacian…

We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the…

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…

The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and…

In this article we discuss a few spectral properties of a paranormal closed operator (not necessarily bounded) defined in a Hilbert space. This class contains closed symmetric operators. First we show that the spectrum of such an operator…

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by…

In this article we consider the one-dimensional Schrodinger operator L(Q) with a Hermitian periodic m by m matrix potential Q. We investigate the bands and gaps of the spectrum and prove that the main part of the positive real axis is…

A periodic lattice distortion that reduces the translational symmetry folds electron bands into a reduced Brillouin zone, leading to band mixing and a tendency to gap formation, as in the Peierls transition in one-dimensional systems.…

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…

A family of spectral decompositions of the spin-weighted spheroidal wave operator is constructed for complex aspherical parameters with bounded imaginary part. As the operator is not symmetric, its spectrum is complex and Jordan chains may…

This paper deals with structural issues concerning wavelet frames and their dual frames. It is known that there exist wavelet frames $\{a^{j/2}\psi( a^j\cdot -kb)\}_{j,k\in \mathbb Z}$ in $L^2(\mathbb R)$ for which no dual frame has wavelet…

Let $G$ be a M\'etivier group and let $N$ be any homogeneous norm on $G$. For $\alpha>0$ denote by $w_\alpha$ the function $e^{-N^\alpha}$ and consider the weighted sub-Laplacian $\mathcal{L}^{w_\alpha}$ associated with the Dirichlet form…

We consider asymptotic behavior of $e^{-itH}f$ for $N$-body Schr\"odinger operator $H=H_0+\sum_{1\le i<j\le N}V_{ij}(x)$ with long- and short-range pair potentials $V_{ij}(x)=V_{ij}^L(x)+V_{ij}^S(x)$ $(x\in {\mathbb R}^\nu)$ such that…