Related papers: Self-Adjointness of Toeplitz Operators on the Sega…

We obtain a Szeg\"o limit theorem for a family of Toeplitz operators defined on the weighted Bergman space of the unit ball $\mathbb{B}_{n}$. The symbols of these operators are supported on some isotropic or co-isotropic submanifold $\Gamma…

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…

We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…

We study radial Carleson--Bergman measures on the unit disk and the corresponding Toeplitz operators acting in the Bergman space. First, we show that such Toeplitz operators are diagonal in the canonical basis, and we compute their…

We provide a sufficient condition for the compactness of a Toeplitz operator acting on the Segal-Bargmann space of vector-valued functions written in terms of an associated operator-valued kernel.

In the context of a weighted graph with vertex set $V$ and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator $\Delta_{\sigma}+W$, where $\Delta_{\sigma}$ is the magnetic Laplacian and…

We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach…

We describe the eigenvalues and eigenvectors of real-analytic, non-self-adjoint Berezin--Toeplitz operators, up to exponentially small error, on complex one-dimensional compact manifolds, under the hypothesis of regularity of the energy…

Some positive results about the composition of Toeplitz operators on the Segal-Bargmann space are presented. A Wick symbol where it is not possible to construct its associated Toeplitz operator is given.

Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous…

We study the boundedness of Toeplitz operators $T_\psi$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $\mathbb{R}^n$. Generalizing earlier results for analytic function spaces, we derive a general…

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on…

We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex $n$-space. This space is characterized by the image of a global Bargmann-type transform introduced by Sj\"ostrand.…

We discuss the self-adjointness in $L^2$-setting of the operators acting as $-\nabla\cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $\Sigma$, without explicit assumptions on the sign of…

In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with bounded symbol is hyponormal if and only if it is…

We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 symbol.We also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary…

Let $M$ be a complete Riemannian manifold and let $\Omega^*(M)$ denote the space of differential forms on $M$. Let $d:\Omega^*(M) \to \Omega^{*+1}(M)$ be the exterior differential operator and let $\Del=dd^*+d^*d$ be the Laplacian. We…

This paper continues the study of paragrassmann algebras begun in Part I with the definition and analysis of Toeplitz operators in the associated holomorphic Segal-Bargmann space. These are defined in the usual way as multiplication by a…

We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators between weighted Sobolev-Fock spaces of polyanalytic functions, which are images of…

For a hyponormal operator, C. R. Putnam's inequality gives an upper bound on the norm of its self-commutator. In the special case of a Toeplitz operator with analytic symbol in the Smirnov space of a domain, there is also a geometric lower…