相关论文: A note on the spectrum of irreducible operators an…

Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…

The spectrum of the singular indefinite Sturm-Liouville operator $$A=\text{\rm sgn}(\cdot)\bigl(-\tfrac{d^2}{dx^2}+q\bigr)$$ with a real potential $q\in L^1(\mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may…

In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory we show that $D$ has point spectrum iff the $\hat A$-genus of its compact dual does not vanish. In this…

We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independent of the perturbation, the residual spectrum is empty, and…

We prove that the spectrum of an n-dimensional semiclassical radial Schr\"odinger operator determines the potential within a large class of potentials for which we assume no symmetry or analyticity. Our proof is based on the first two…

This paper contributes to the analysis of the peripheral (point) spectrum of positive linear operators on Banach lattices. We show that, under appropriate growth and regularity conditions, the peripheral point spectrum of a positive…

We show that, given a closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_n\to\infty$ with the following property: if $T$ is a Hilbert-space contraction such that $\sigma(T)\subset E$ and…

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the…

For a linear operator $T$ in a Banach space let $\sigma_p(T)$ denote the point spectrum of $T$, $\sigma_{p[n]}(T)$ for finite $n > 0$ be the set of all $\lambda \in \sigma_p(T)$ such that $\dim \ker (T - \lambda) = n$ and let…

For an unramified connected reductive group $G$ defined over a number field $F$, consider the part of the spherical automorphic spectrum with cuspidal support $[T,\mathcal{O}(\chi)]$, where $T$ is a maximal torus and $\chi$ is an unramified…

In a thin multidimensional layer we consider a second order differential PT-symmetric operator. The operator is of rather general form and its coefficients are arbitrary functions depending both on slow and fast variables. The PT-symmetry…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…

For simple connected graphs with incommensurate bond lengths and with unitary symmetry we prove the Bohigas-Giannoni-Schmit conjecture in its most general form. Using supersymmetry and taking the limit of infinite graph size, we show that…

An operator $A$ on an $l^p$-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. The coset of $A$ in the Calkin algebra determines, for example, the Fredholmness…

We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to…

We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free…

In this paper, we provide the spectral decomposition in Hilbert space of the $\mathcal{C}_0$-semigroup $P$ and its adjoint $\hatP$ having as generator, respectively, the Caputo and the right-sided Riemann-Liouville fractional derivatives of…

The goal of this note is to study the spectrum of a self-adjoint convolution operator in $L^2(\mathbb R^d)$ with an integrable kernel that is perturbed by an essentially bounded real-valued potential tending to zero at infinity. We show…