Related papers: Toeplitz operators and Hamiltonian torus action

We study Toeplitz operators on the Bargmann space, whose Toeplitz symbols are exponentials of complex inhomogeneous quadratic polynomials. Extending a result by Coburn--Hitrik--Sj\"{o}strand, we show that the boundedness of such Toeplitz…

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…

In the case of a compact real analytic symplectic manifold M we describe an approach to the complexification of Hamiltonian flows [Se, Do1, Th1] and corresponding geodesics on the space of Kahler metrics. In this approach, motivated by…

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…

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

We introduce an extended class of cross-Toeplitz operators which act between Fock--Segal--Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group.…

Motivated by the canonical decomposition of contractions on Hilbert spaces, we investigate when contractive Toeplitz operators on vector-valued Hardy spaces on the unit disc admit a non-zero reducing subspace on which its restriction is…

We study the ranks of commutators and generalized semicommutators of Toeplitz operators with quasihomogeneous symbols on both the harmonic Bergman space and the Bergman Space. In particular, when one of quasihomogeneous symbols is the the…

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds…

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…

In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on…

For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given…

We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…

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…

Let K be a connected compact semisimple Lie group and Kc its complexification. The generalized Segal-Bargmann space for Kc, is a space of square-integrable holomorphic functions on Kc, with respect to a K-invariant heat kernel measure. This…

Let $R$ be a compact Riemann surface and $\Gamma$ be a Jordan curve separating $R$ into connected components $\Sigma_1$ and $\Sigma_2$. We consider Calder\'on-Zygmund type operators $T(\Sigma_1,\Sigma_k)$ taking the space of $L^2$…

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…

For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant $\hbar$…

In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the…

We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in $\mathbb{C}^2$ and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that…