Related papers: A local Szeg\"o-type theorem in Toeplitz quantizat…
A Weyl law for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. In the setting of positive line bundles, we revisit this theme in light of local asymptotic techniques based on the microlocal…
A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of…
We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore,…
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…
We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise…
Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szeg\"o…
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szeg\H{o}-type spectral…
In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for…
We present an equivariant generalization of Boutet de Monvel's index theorem for Toeplitz operators on contact manifolds. We prove that the Dirac operator and the Szeg\"o projection determine the same class in equivariant $K$-homology,…
The classical Szeg\"o theorems study the asymptotic behaviour of the determinants of the finite sections $P_n T(a) P_n$ of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results…
In this paper, we study the relations between the log term of the Szeg\"o kernel of the unit circle bundle of the dual line bundle of an ample line bundle over a compact K\"ahlermanifold. We proved a local rigidity theorem. The result is…
We give a simple proof of Tian's theorem that the Kodaira embeddings associated to a positive line bundle over a compact complex manifold are asymptotically isometric. The proof is based on the diagonal asymptotics of the Szego kernel (i.e.…
We obtain Szeg\H{o}-type Limit Theorems in the setting of Reproducing Kernel Hilbert Spaces on discs in $\mathbb{C}$. From this, we derive a formula for the density of the eigenvalues of compressions of Toeplitz operators. Examples for the…
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…
We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of ${\mathbb C}^N$ . We compute asymptotically the moments of their spectral measures, and we prove Szeg\"o limit theorems…
We discuss generalizations of the Szeg\H{o} Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems.…
In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of…
We state and prove a version of Szeg\H{o}'s first limit theorem for Toeplitz-like operators on the Drury-Arveson space in the unit ball.
We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…
We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over K\"ahler…