Related papers: An exotic calculus of Berezin-Toeplitz operators

We generalize some earlier results on a Berezin-Toeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and…

In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…

This paper studies the \(k^{th}-\)order slant Toeplitz and slant little Hankel operators on the weighted Bergman space \(\mathcal{A}_\alpha^2(\mathbb{D})\). These operators are constructed using a slant shift operator \(W_k\) composed with…

In this thesis, we introduce complex manifolds with local spectral gaps and study their asymptotic behavior using the scaling method. With these asymptotics, we obtain an asymptotic expansion for the Bergman kernel of a Hermitian…

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…

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 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…

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in…

It is well known that a Toeplitz operator is invertible if and only if its symbols admits a canonical Wiener-Hopf factorization, where the factors satisfy certain conditions. A similar result holds also for singular integral operators. More…

In this paper, we show that the semiclassical calculus recently developed on nilpotent Lie groups and nilmanifolds include the functional calculus of suitable subelliptic operators. Moreover, we obtain Weyl laws for these operators. Amongst…

Classical pseudo-differential calculus on $\mathbb{R}^{d}$ can be viewed as a (non-commutative) functional calculus for the standard position and momentum operators $(Q_{1}, \dots , Q_{d})$ and $(P_{1}, \dots , P_{d})$. We generalise this…

This work focuses on the analysis of the spectral $\zeta$-function associated with a Schr\"{o}dinger operator endowed with a P\"oschl--Teller potential. We construct the spectral $\zeta$-function using a contour integral representation and,…

We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…

Inspired by our previous work on the boundedness of Toeplitz operators, we introduce weak BMO and VMO type conditions, denoted by BWMO and VWMO, respectively, for functions on the open unit disc of the complex plane. We show that the…

In the present article, we study the discrete spectrum of certain bounded Toeplitz operators with harmonic symbol on a Bergman space. Using the methods of classical perturbaton theory and recent results by Borichev-Golinskii-Kupin and…

This dissertation focuses on developing a new construction of a functional calculus using Henstock-Kurzweil integration methods. The assignment of a functional calculus will be applied to self-adjoint operators. We will address both the…

We consider Toeplitz operators in Bergman and Fock type spaces of polyanalytic $L^2\textup{-}$functions on the disk or on the half-plane with respect to the Lebesgue measure (resp., on $\mathbb{C}$ with the plane Gaussian measure). The…

Let $(M,J,\omega)$ be a quantizable compact K\"ahler manifold, with quantizing Hermitian line bundle $(A,h)$, and associated Hardy space $H(X)$, where $X$ is the unit circle bundle. Given a collection of $r$ Poisson commuting quantizable…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…