arXiv subjects

Puyu Cui

Publications and source records attributed to Puyu Cui.

3 recordsLinked to original sources

arXiv2026

Norm of the Hilbert Matrix Operator on Bloch-Type Spaces

We determine the exact norm of the Hilbert matrix operator $\mathcal H$ on the $α$-Bloch space $\mathcal B^α$ for $1<α<2$, together with all norm-attaining functions of norm one. For $1<α\leq3/2$, we obtain an explicit formula for the exact norm in terms of the Gamma function. For $3/2<α<2$, we obtain an exact one-dimensional maximization formula and show that the corresponding maximum is attained at an interior point of $(0,1)$. We also determine the exact norm of $\mathcal H:\mathcal B^α\to\mathcal B^α_{\log}$. The norm formula changes at the critical parameter $α=4/3$, and the exact norm is obtained for the full range $1<α<2$. The norm-attaining functions are completely characterized for both operators.

math.FA↗

arXiv2026

Spectral properties of Toeplitz operators with harmonic function symbols on the Bergman space

This paper investigates the spectral properties of Toeplitz operators on the Bergman space of unit disk. We present an integral representation of $ T^*_{z^m}$, which establishes a connection between the Bergman functions and the solutions of PDE theory. In fact, by leveraging the Poincaré theorem in difference equations and the solution forms of differential equations, this paper describes the kernels of certain Toeplitz operators with harmonic polynomial symbols, and further gives the sufficient conditions for the connectedness of the spectra of these Toeplitz operators. The spectral properties of $ T_φ$ with $φ(z) =\overline{z}^{m} + αz^m + β$ are characterized, such as $σ(T_φ)= \overline{φ(\mathbb {D})}$, Fredholm index of $T_φ$ can only be one of $m,-m$ and $0$, $T_φ$ satisfies Coburn's theorem. These findings offer an illuminating example for the essential projective spectra of non-commuting operators.

math.FA↗

arXiv2009

Chaos for Cowen-Douglas operators

In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces.

math.FA↗