Related papers: Generalized spectrum of second order differential …
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…
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…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
We consider a class of Hankel operators $H$ realized in the space $L^2 ({\Bbb R}_{+}) $ as integral operators with kernels $h(t+s)$ where $h(t)=P (\ln t) t ^{-1}$ and $P(X)= X^n+p_{n-1} X^{n-1}+\cdots$ is an arbitrary real polynomial of…
In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a…
We consider a spectral stability estimate by Burenkov and Lamberti concerning the variation of the eigenvalues of second order uniformly elliptic operators on variable open sets in the N-dimensional euclidean space, and we prove that it is…
We study the spectral theory of operators, generated as direct sums of self-adjoint extensions of quasi-differential minimal operators on a multi-interval set (self-adjoint vector-operators), acting in a Hilbert space. Spectral theorems for…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
The equivalence problem for linear differential operators of the second order, acting in vector bundles, is discussed. The field of rational invariants of symbols is described and connections, naturally accosiated with differential…
In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
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…
We approximate the spectra of a class of $2n$-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of differential operators such as those arising in elliptic, biharmonic,…
We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.
In this paper, we describe the spectrum properties of mixed operators, precisely the superposition of the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is \begin{equation}…
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic…
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continuous on some subsets of the complex plane and we provide…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…