Related papers: Spectral properties of integral operators in probl…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
We obtain spectral inequalities and asymptotic formulae for the discrete spectrum of the operator $\frac12\, \log(-\Delta)$ in an open set $\Omega\in\Bbb R^d$, $d\ge2$, of finite measure with Dirichlet boundary conditions. We also derive…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
This thesis is devoted to asymptotic norm estimates for oscillatory integral operators acting on the L^2 space of functions of one real variable. The operators in question have compact support and an oscillatory kernel of the form exp(i…
In this paper we discuss the spectral properties of one-term symmetric differential operators of even order with interior singularity, namely, we determine the deficiency numbers, describe its self-adjoint extensions and their spectrum. It…
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…
We consider the spectral problem of the Lax pair associated to periodic integrable partial differential equations. We assume this spectral problem to be a polynomial of degree $d$ in the spectral parameter $\lambda$. From this assumption,…
We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.
We study the semi-classical behavior of the spectral function of the Schr\"{o}dinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
Each bounded operator T on an infinite dimensional Hilbert space H is a sum of three operators that are similar to positive operators; two such operators are sufficient if T is not a compact perturbation of a scalar. The spectra of L\"uders…
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…