Related papers: Functional calculus and quantization commutes with…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…
In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy…
We consider a natural variant of Berezin-Toeplitz quantization of compact K\"{a}hler manifolds, in the presence of a Hamiltonian circle action lifting to the quantizing line bundle. Assuming that the moment map is positive, we study the…
Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and $\mathbb C^n$ are discussed. Results are presented on the asymptotics \begin{align*} \|…
In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an $n$-tuple $T$ of not necessarily commuting operators. This calculus is different from the one discussed in…
Given a polyanalytic function, we show that the corresponding Toeplitz operator on the Bergman space of the unit disc can be expressed as a quotient of certain differential operators with holomorphic coefficients. This enables us to obtain…
We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…
A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute…
Let $M$ be an arbitrary complex manifold and let $L$ be a Hermitian holomorphic line bundle over $M$. We introduce the Berezin-Toeplitz quantization of the open set of $M$ where the curvature on $L$ is non-degenerate. The quantum spaces are…
One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb{D}$ in the complex place $\mathbb{C}$ is to completely describe the commutant of a given Toeplitz operator, that is, the set of all…
Harmonic analysis on a toric Kahler variety M refers to the orthonormal basis of eigenfunctions of the complex torus action on the spaces H^0(M, L^N) of holomorphic sections of powers of a positive line bundle L and the Fourier multipliers…
This talk reports on results on the deformation quantization (star products) and on approximative operator representations for quantizable compact K"ahler manifolds obtained via Berezin-Toeplitz operators. After choosing a holomorphic…
Let $X$ be a compact connected orientable CR manifold with the action of a connected compact Lie group $G$. Under natural pseudoconvexity assumptions we show that the CR Guillemin-Strernberg map is Fredholm at the level of Sobolev spaces of…
Toeplitz operators on spaces $H^p(G)\ (1< p<\infty)$ associated with compact connected Abelian group $G$ with ordered dual are considered and the generalization of the classical Gohberg-Krein theorem on the Fredholm index of such operators…
Let $X$ be a compact connected CR manifold of dimension $2n-1, n\geq 2$ with a transversal CR $S^1$-action on $X$. We study the Fourier components of the Kohn-Rossi cohomology with respect to the $S^1$-action. By studying the Szeg\"o kernel…
We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function $\omega$ and suitable window function $\fy $, the Toeplitz operator (or localization operator) $\tp_\fy…
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…
We demonstrate that the weight operator associated with a submultiplicative filtration on the section ring of a polarized complex projective manifold is a Toeplitz operator. We further analyze the asymptotics of the associated weighted…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
As a class of compact operators on the $\ell^2-$valued Bergman space $A^2_\alpha (\mathbb B_n, \ell^2)$ on the unit ball $\mathbb B_n,$ we study Toeplitz operators with $BMO^1_\alpha (\mathbb B_n, \mathcal L(\ell^2))$ operator-valued…