Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2019-12-02 , DOI: 10.1016/j.bulsci.2019.102826 Aneesh Mundayadan , Jaydeb Sarkar
Complementing earlier results on dynamics of unilateral weighted shifts, we obtain a sufficient (but not necessary, with supporting examples) condition for hypercyclicity, mixing and chaos for , the adjoint of , on vector-valued analytic reproducing kernel Hilbert spaces in terms of the derivatives of kernel functions on the open unit disc in . Here denotes the multiplication operator by the coordinate function z, that is for all and . We analyze the special case of quasi-scalar reproducing kernel Hilbert spaces. We also present a complete characterization of hypercyclicity of on tridiagonal reproducing kernel Hilbert spaces and some special classes of vector-valued analytic reproducing kernel Hilbert spaces.
中文翻译:
再现内核希尔伯特空间中的线性动力学
补充早期关于单边加权平移动力学的结果,我们获得了超循环性,混合和混沌的充分(但不是必须的,有支持的例子)条件 ,的伴随物 ,在向量值分析再现核希尔伯特空间上 就开放单元光盘上的内核函数的导数而言 在 。这里用坐标函数z表示乘法算子,即 对所有人 和 。我们分析了准标量重现内核希尔伯特空间的特殊情况。我们还提出了一个完整的表征 关于三对角重现核希尔伯特空间和一些特殊类的向量值解析重现核希尔伯特空间。