arXiv subjects
Publications and source records attributed to Yong-Xin Gao.
In this paper, we provide complete characterizations for the spectrum, essential spectrum, and point spectrum of the generators of weighted composition $C_0$-semigroups induced by hyperbolic semiflows on Bergman spaces. We give an explicit example showing that the spectral properties can be influenced by the behavior of the semigroup near non-fixed self-contact points.
In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.
In this paper we give precise characterizations of the relation between the Nevanlinna counting function and pull-back measure of an analytic self-map of the unit disk near the boundary. We show that it is quite worth considering these two concepts on the maximal ideal space of the bounded analytic functions.
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.
In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces $A_α^2(\mathbb{D})$.
In this paper we give the answers to two open questions on complex symmetric composition operators. By doing this, we give a complete description of complex symmetric composition operators whose symbols are linear fractional.
In this paper we show that a composition operator $C_φ$ cannot be complex symmetric on Hardy-Hilbert space $H^2(D)$ when $φ$ is an elliptic automorphism of order $3$ and not a rotation. This completes the project of finding all invertible composition operators which are complex symmetric $H^2(D)$.
In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_α^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit ball of the $N$-dimensional complex space. By taking $N=1$, $\mathbb{B}_N=\mathbb{D}$ the unit disc, we also complete the discussion about the spectrum of a weighted composition operator when it is invertible on $H^2(\mathbb{D})$ or $A_α^2(\mathbb{D})$.