Related papers: Toeplitz operators defined by sesquilinear forms: …
We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $\alpha\in\mathbb{R}$. We give characterizations of bounded and…
We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the…
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…
The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol…
We obtain the semi-classical expansion of the kernels and traces of Toeplitz operators with $\cC^k$--\,symbol on a symplectic manifold. We also give a semi-classical estimate of the distance of a Toeplitz operator to the space of…
For a partition $\boldsymbol{k} = (k_1, \dots, k_m)$ of $n$ consider the group $\mathrm{U}(\boldsymbol{k}) = \mathrm{U}(k_1) \times \dots \times \mathrm{U}(k_m)$ block diagonally embedded in $\mathrm{U}(n)$ and the center $\mathbb{T}^m$ of…
Let $0<\alpha,\beta,t<\infty$ and $\mu$ be a positive Borel measure on $\mathbb{C}^n$. We consider the Berezin-type operator $S^{t,\alpha,\beta}_{\mu}$ defined by…
We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz…
In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining…
In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is…
The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
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…
On the unit ball B^n we consider the weighted Bergman spaces H_\lambda and their Toeplitz operators with bounded symbols. It is known from our previous work that if a closed subgroup H of \widetilde{\SU(n,1)} has a multiplicity-free…
In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson…
We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the…
Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct…
Using the model theory for Toeplitz operators with smooth symbols developed by the fourth author in the 80's, we study whether such operators $T_{F}$ can be embedded into a $C_{0}$-semigroup of operators on the Hardy space $H^p$ of the open…
We use quantum harmonic analysis and representation theory to provide a new proof of Xia's theorem: "Toeplitz operators are norm dense in the Toeplitz algebra over the Bergman space of the unit ball."
We study the asymptotic expansion of the product of two Toeplitz operators on the Fock space. In comparison to earlier results we require significantly less derivatives and get the expansion to arbitrary order. This, in particular, improves…