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Related papers: Subprincipal symbol for Toeplitz operators

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We consider symmetric separately radial (with corresponding group $S_n\rtimes \mathbb{T}^n$) and alternating separately radial (with corresponding group $A_n\rtimes \mathbb{T}^n$) symbols, as well as the associated Toeplitz operators on the…

Functional Analysis · Mathematics 2024-03-14 Armando Sánchez-Nungaray , José Rosales-Ortega , Carlos González-Flores

In this paper we characterize the compact operators on the Bergman space $A^p(\mathbb{D}^n)$. The main result shows that an operator on $A^p(\mathbb{D}^n)$ is compact if and only if it belongs to the Toeplitz algebra $\mathcal{T}_{p}$ and…

Complex Variables · Mathematics 2013-08-20 Mishko Mitkovski , Brett D. Wick

For phase-space manifolds which are compact Kaehler manifolds relations between the Berezin-Toeplitz quantization and the quantization with the help of Berezin's coherent states and symbols are studied. First the results on the…

Quantum Algebra · Mathematics 2016-09-07 Martin Schlichenmaier

We study Toeplitz operators with uniformly continuous symbols on generalized harmonic Bergman spaces of the unit ball in $\mathbb{R}^n$. We describe their essential spectra and establish a short exact sequence associated with the…

Functional Analysis · Mathematics 2010-04-07 Trieu Le

In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1<p<\infty$ and $\alpha>-1$. The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz…

Classical Analysis and ODEs · Mathematics 2013-01-22 Mishko Mitkovski , Daniel Suárez , Brett D. Wick

An approach to the construction of index formulas for elliptic operators on singular manifolds is suggested on the basis of K-theory of algebras and cyclic cohomology. The equivalence of Toeplitz and pseudodifferential quantizations, well…

Analysis of PDEs · Mathematics 2011-11-08 V. Nazaikinskii , G. Rozenblum , A. Savin , B. Sternin

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…

Functional Analysis · Mathematics 2016-05-24 Grigori Rozenblum , Nikolai Vasilevski

In this note, we show that for hyponormal Toeplitz operators, there exists a lower bound for the area of the spectrum. This extends the known estimate for the spectral area of Toeplitz operators with an analytic symbol.

Complex Variables · Mathematics 2015-09-01 Cheng Chu , Dmitry Khavinson

We investigate a class of operators resulting from a quantization scheme attributed to Berezin. These so-called Berezin-Toeplitz operators are defined on a Hilbert space of square-integrable holomorphic sections in a line bundle over the…

Mathematical Physics · Physics 2009-11-07 Bernhard G. Bodmann

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…

Functional Analysis · Mathematics 2018-07-31 Grigori Rozenblum , Nikolai Vasilevski

We study the boundedness of Toeplitz operators $T_\psi$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $\mathbb{R}^n$. Generalizing earlier results for analytic function spaces, we derive a general…

Functional Analysis · Mathematics 2022-03-15 Raffael Hagger , Congwen Liu , Jari Taskinen , Jani A. Virtanen

We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the spaces of holomorphic sections of a prequantizing line bundle over compact K\"ahler manifolds under deformations of the complex structure. We show that the…

Differential Geometry · Mathematics 2021-07-14 Louis Ioos

We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…

Functional Analysis · Mathematics 2016-01-27 Raul Quiroga-Barranco

In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a…

Functional Analysis · Mathematics 2016-07-05 Akaki Tikaradze

In this article, we state the Bohr-Sommerfeld conditions around a global minimum of the principal symbol of a self-adjoint semiclassical Toeplitz operator on a compact connected K\"ahler surface, using an argument of normal form which is…

Spectral Theory · Mathematics 2012-09-28 Yohann Le Floch

In the semiclassical limit, it is well-known that the first eigenvector of a Toeplitz operator concentrates on the minimal set of the symbol. In this paper, we give a more precise criterion for concentration in the case where the minimal…

Spectral Theory · Mathematics 2018-03-08 Alix Deleporte

The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded…

Functional Analysis · Mathematics 2014-05-23 Grigori Rozenblum , Nikolai Vasilevski

This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum,…

Functional Analysis · Mathematics 2020-02-21 G. J. Groenewald , S. ter Horst , J. Jaftha , A. C. M. Ran

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…

Classical Analysis and ODEs · Mathematics 2025-10-23 David Békollè , Hugues Olivier Défo , Edgar L. Tchoundja

We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…

Mathematical Physics · Physics 2019-05-07 Shin Hayashi