Related papers: Berezin-Toeplitz quantization revisited

In the present paper, we study the boundedness and compactness of Toeplitz operators and Berezin-type operators between different weighted Bergman spaces over tubular domains in $\mathbb{C}^n$. We establish their connection with Carleson…

For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. For Bernstein-Markov measures, this results in the…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…

On a prequantizable K\"ahler manifold $(M, \omega, L)$, Chan-Leung-Li constructed a genuine (non-asymptotic) action of a subalgebra of the Berezin-Toeplitz star product on $H^0(M, L^{\otimes k})$ for each level $k$ [14]. We extend their…

In this paper, we provide a complete characterization of bounded Toeplitz operators $T_f$ on the harmonic Bergman space of the unit disk, where the symbol $f$ has a polar decomposition truncated above, that commute with $T_{z+\bar{g}}$, for…

We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, and use it to completely characterize boundedness and compactness of Hankel operators on weighted Fock spaces. As an…

A well known result of Brown and Halmos shows that the Toeplitz operators induced by $L^{\infty}(\mathbb T)$ symbols on the Hardy space of the unit disc $\mathbb D$ are characterized by the operator identity $T_{\bar{z}}AT_z=A,$ where $T_z,…

Let $X$ be the unit circle bundle of a positive line bundle on a Hodge manifold. We study the local scaling asymptotics of the smoothed spectral projectors associated to a first order elliptic T\"{o}plitz operator $T$ on $X$, possibly in…

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…

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…

In this survey article we consider the operator pair $(H,H_0)$ where $H_0$ is the shifted 3D Schr\"odinger operator with constant magnetic field, $H : = H_0 + V$, and $V$ is a short-range electric potential of a fixed sign. We describe the…

Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of…

Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an…

In this paper we consider the generalized little Hankel and Berezin type operators on Besov spaces of holomorphic functions on polydiscs and give results about the boundedness of these operators.

Let $(X, T^{1,0}X)$ be a connected orientable compact CR manifold of dimension $2n+1$, $n \geq 1$ with non-degenerate Levi curvature. In this paper, we study the algebra of Toeplitz operators on $X$ and we establish star product for some…

In this paper, we extend the Brown-Halmos theorems to the Fock space and investigate the range of the Berezin transform. We observe that there are non-pluriharmonic functions $u$ that can be written as a finite sum…

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…

We characterize the nuclearity of Toeplitz operators $T_\mu: F_\alpha^p \to F_\alpha^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For positive measures $\mu$ and $q\leq p$, we provide necessary and sufficient conditions in…

For a real symmetric domain $G_{\mathbb R}/K_{\mathbb R}$, with complexification $G_{\mathbb C}/K_{\mathbb C}$, we introduce the concept of "star-restriction" (a real analogue of the "star-products" for quantization of K\"ahler manifolds)…

We prove sufficient conditions for the boundedness and compactness of Toeplitz operators $T_a$ in weighted sup-normed Banach spaces $H_v^\infty$ of holomorphic functions defined on the open unit disc $\mathbb{D}$ of the complex plane; both…