arXiv subjects

Xing-Tang Dong

Publications and source records attributed to Xing-Tang Dong.

4 recordsLinked to original sources

arXiv2020

Essential Spectra of Weighted Composition Operators Induces by Elliptic Automorphisms

The spectrum of a weighted composition operator $C_{ψ, φ}$ who is induced by an automorphism has been investigated for over fifty years. However, many results are got only under the condition that the weight function $ψ$ is continuous up to the boundary. In this paper we study the spectra and essential spectra of $C_{ψ,φ}$ on weighted Bergman spaces when $φ$ is an elliptic automorphism, without the assumption that $ψ$ is continuous up to the boundary.

math.FA↗

arXiv2018

Monomial-type Toeplitz operators on some weakly pseudoconvex domains

In this paper, we completely characterize the finite rank commutator and semi-commutator of two monomial-type Toeplitz operators on the Bergman space of certain weakly pseudoconvex domains. Somewhat surprisingly, there are not only plenty of commuting monomial-type Toeplitz operators but also non-trivial semi-commuting monomial-type Toeplitz operators. Our results are new even for the unit ball.%The situation is different from the case of unit disk. %Our results extend several known results using completely different arguments. Some interesting higher-dimensional phenomena appear on the unit polydisk.

math.FA↗

arXiv2016

The Fourier and Hilbert transforms under the Bargmann transform

There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on $L^2(\R)$, including the fractional Fourier transform, the fractional Hilbert transform, and the wavelet transform.

math.CV↗

arXiv2016

Ranks of Commutators and Generalized Semicommutators of Quasihomogeneous Toeplitz Operators

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 form of $e^{ikθ}r^{m}$, we first obtain specific sufficient and necessary conditions for commutators and generalized semicommutators to be finite rank. Then we make further efforts to determine the range of each finite rank commutator and generalized semicommutators, and consequently the explicit canonical form and the rank are obtained. Thus, the finite rank problem of commutators and generalized semicommutators of such special Toeplitz operators is completely solved. As applications, several interesting corollaries and nontrivial examples are given. Also, we show close connections of the finite rank problem between the harmonic Bergman space and Bergman space cases.

math.FA↗