Related papers: Spectral algebraic curves and decomposable operato…
We consider the self-adjoint third order operator with 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers the real line. We determine the high energy asymptotics of the periodic,…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous $2$-cocycle one associates the reduced twisted groupoid $C^*$-algebra. Elements (or multipliers) of this algebra admit…
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…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
We study the spectrum of Laplace operators on a one-parameter family of gravitational instantons of bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The family of geometries includes the Taub-NUT,…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
We consider operators $H_\mu$ of convolution with measures $\mu$ on locally compact groups. We characterize the spectrum of $H_\mu$ by constructing auxiliary operators whose kernel contain the pure point and singular subspaces of $H_\mu$,…
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral…
Negative-index metamaterials possess a negative refractive index and thus present an interesting substance for designing uncommon optical effects such as invisibility cloaking. This paper deals with operators encountered in an…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
We characterize the set of diagonals of the unitary orbit of a self-adjoint operator with a finite spectrum. Our result extends the Schur-Horn theorem from a finite dimensional setting to an infinite dimensional Hilbert space analogous to…
It is well-known that, in general, an appearance of an algebraic hypersurface of finite multiplicity in the projective joint spectrum of an operator tuple does not imply the existence of a finite-dimensional common invariant subspace.We…
We study the (H\"older-)continuous behavior of the spectra belonging to a family of linear bounded operators $(A_t)_{t\in T}$ indexed by a topological space $T$. For the cases of self-adjoint, unitary and normal operators, a…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
In this paper we present some spectral property for quotient bounded operators and locally bounded operators on locally convex spaces. We introduce the spectral radius of a quotient bounded operator and we show that the Gelfand formula for…
Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this…
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on…
The first half of this mostly expository note reviews some notions of joint spectrum of linear operators, and it gives a new characterization of amenable groups in terms of projective spectrum. The second half revisits an application of…