复合算子序列的频繁超循环函数子空间

Growth of (frequently) hypercyclic entire functions for differential operators

We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions of these functions on particular rays or sectors. Our research extends known results in several respects.

Complete systems of partial derivatives of entire functions and frequently hypercyclic operators

We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space $H(\mathbb{C}^d)$ of all entire functions of $d$ variables. As an appliation of this result we describe new classes of frequently hypercyclic operators on $H(\mathbb{C}^d)$.

整函数的增长：从频繁超循环性到微分算子的超循环性

Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator

本文研究微分算子下频繁超循环整函数的增长速度，建立其与超循环整函数最小增长的联系，并证明所得结果具有最优性。

频繁超循环整函数与缓慢增长

Frequently hypercyclic meromorphic curves with slow growth

研究通过Nevanlinna理论和Oka原理，构造了在射影空间中具有缓慢增长的频繁超循环整函数，并揭示了在增长约束下频繁超循环性质的二元对立。

On the intersection of the spectrum of frequently hypercyclic operators with the unit circle

We exclude the existence of frequently hypercyclic operators that have a spectrum contained in the closed unit disc and that intersects the unit circle in only finitely many points under certain additional conditions. This extends a result of S. Shkarin, which states that the spectrum of a frequently hypercyclic operator cannot have isolated points.

Optimal growth of frequently hypercyclic entire functions

We solve a problem posed by A. Bonilla and K.-G. Grosse-Erdmann by constructing an entire function $f$ that is frequently hypercyclic with respect to the differentiation operator, and satisfies $M_f(r)\leq\displaystyle ce^r r^{-1/4}$, where $c>0$ be chosen arbirarily small. The obtained growth rate is sharp. We also obtain optimal results for the growth when measured in terms of average $L^p$-norms. Among other things, the proof applies Rudin-Shapiro polynomials and heat kernel estimates.