Related papers: Unbounded integral Hankel operators
We prove a bound, of Bargmann- Birman-Schwinger type, on the number of eigenvalues of the matrix Schr\"odinger operator on the half line, with the most general self adjoint boundary condition at the origin, and with selfadjoint matrix…
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…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
In this article we consider the generalized integral operators acting on the Hilbert space $H^2$. We characterize when these operators are uniform, strong and weakly asymptotic Toeplitz and Hankel operators. Moreover we completely describe…
Let ${\mathcal A}$ be the class of functions that are analytic in the unit disc ${\mathbb D}$, normalized such that $f(z)=z+\sum_{n=2}^\infty a_nz^n$, and let class ${\mathcal U}(\lambda)$, $0<\lambda\le1$, consists of functions…
In this paper, we specify what functions induce the bounded composition operators on a reproducing kernel Hilbert space (RKHS) associated with an analytic positive definite function defined on $\mathbf{R}^d$. We prove that only affine…
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…
In this dissertation we explore the $[L^{\mathrm{p}},\ L^{q}]$-boundedness of certain integral operators on weighted spaces on cones in ${\mathbb R}^{n}.$ These integral operators are of the type $\displaystyle \int_{V}k(x,\ y)f(y)dy$…
This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of self-adjoint operators. Our main results are the…
We obtain several essential self-adjointness conditions for a Schroedinger type operator D*D+V acting in sections of a vector bundle over a manifold M. Here V is a locally square-integrable bundle map. Our conditions are expressed in terms…
We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the nonnegative real numbers and describe their basic properties. Using Toeplitz operators and the…
We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on a Hilbert space. As applications, we characterize compactness of affine and Weyl-Heisenberg localization operators as well as…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
We prove smoothing properties along suitable directions of the Ornstein-Uhlenbeck evolution operator, namely the evolution operator associated to non autonomous Ornstein-Uhlenbeck equations. Moreover we use such smoothing estimates to prove…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while…
We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional…
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
Using several complex variables techniques, we investigate the interplay between the geometry of the boundary and compactness of Hankel operators. Let f be a function smooth up to the boundary on a smooth bounded pseudoconvex domain D in…