Related papers: An inverse spectral problem for non-compact Hankel…
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…
The spectral properties of a class of band matrices are investigated. The reconstruction of matrices of this special class from given spectral data is also studied. Necessary and sufficient conditions for that reconstruction are found. The…
We consider the class of bounded self-adjoint Hankel operators $\mathbf H$, realised as integral operators on the positive semi-axis, that commute with dilations by a fixed factor. By analogy with the spectral theory of periodic…
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…
We consider smooth vector bundles over smooth manifolds equipped with non-smooth geometric data. For nilpotent differential operators acting on these bundles, we show that the kernels of induced Hodge-Dirac-type operators remain isomorphic…
Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…
Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on $\cn$. The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that…
It was shown by M. I. Zelikin (2007) that the spectrum of a nuclear operator in a separable Hilbert space is central-symmetric iff the spectral traces of all odd powers of the operator equal zero. The criterium can not be extended to the…
In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of…
We introduce and study a natural non-commutative generalization of \(\mu\)-Hankel operators originally defined on Hardy spaces over compact abelian groups. Within the framework of Peter-Weyl theory, we define matrix-valued Hankel operators…
We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
Suppose $\mathcal{A}$ is a compact normal operator on a Hilbert space $H$ with certain lacunarity condition on the spectrum (which means, in particular, that its eigenvalues go to zero exponentially fast), and let $\mathcal{L}$ be its rank…
We describe large classes of compact self-adjoint Hankel operators whose eigenvalues have power asymptotics and obtain explicit expressions for the coefficient in front of the leading term. The results are stated both in the discrete and…
We study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators. The problems under consideration include completeness of eigenvectors, relations between completeness of the perturbed operator and its…
Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…
We establish a general link between integrable systems in algebraic geometry (expressed as Jacobian flows on spectral curves) and soliton equations (expressed as evolution equations on flat connections). Our main result is a natural…
The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form $-d^2/dx^2+V(g;x)$, where the potential is an elliptic function depending on a coupling vector $g\in{\mathbb R}^4$.…
We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\mathbb{R}^d$ and characterize solvability of the problem in terms of the…
We consider the complex solvable non-commutative two dimensional Lie algebra $L$, $L=<y>\oplus <x>$, with Lie bracket $[x,y]=y$, as linear bounded operators acting on a complex Hilbert space $H$. Under the assumption $R(y)$ closed, we…