HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL

Garcia A. G.; Hernandez-Medina M. A.; Portal A.

首页> 外文期刊>Osaka Journal of Mathematics >HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL

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HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL

机译：解析希尔伯特-空值核诱导的整函数的希尔伯特空间中翻译算子的超循环

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The study of the hypercyclicity of an operator is an old problem in mathematics; it goes back to a paper of Birkhoff in 1929 proving the hypercyclicity of the translation operators in the space of all entire functions with the topology of uniform convergence on compact subsets. This article studies the hypercyclicity of translation operators in some general reproducing kernel Hilbert spaces of entire functions. These spaces are obtained by duality in a complex separable Hilbert space H by means of an analytic H-valued kernel. A link with the theory of de Branges spaces is also established. An illustrative example taken from the Hamburger moment problem theory is included.

机译：对算子超循环性的研究是数学中的一个老问题。它可以追溯到1929年伯克霍夫（Birkhoff）的论文，证明了翻译算子在所有函数的空间中具有超循环性，并且在紧凑子集上具有统一收敛的拓扑。本文研究了在某些具有完整功能的通用再现内核希尔伯特空间中翻译算符的超循环性。这些空间是通过解析H值核在复杂的可分离希尔伯特空间H中通过对偶获得的。还建立了与de Branges空间理论的联系。包括从汉堡矩问题理论中获得的说明性示例。

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《Osaka Journal of Mathematics》 |2015年第3期|共19页
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Garcia A. G.; Hernandez-Medina M. A.; Portal A.;
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1. HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL [J] . Garcia A. G., Hernandez-Medina M. A., Portal A. Osaka Journal of Mathematics . 2015,第3期

机译：解析希尔伯特-空值核诱导的整函数的希尔伯特空间中翻译算子的超循环
2. The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions [J] . Rosenfeld Joel A., Russo Benjamin, Dixon Warren E. Journal of Mathematical Analysis and Applications . 2018,第2期

机译：Mittag Leffler再现整个和分析功能的内核Hilbert空间
3. Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels [J] . Hong-Wei Sun, Ding-Xuan Zhou Journal of Fourier Analysis and Applications . 2008,第1期

机译：再现与解析平移不变Mercer内核相关的内核希尔伯特空间
4. Kernel-Induced Sampling Theorem for Translation-Invariant Reproducing Kernel Hilbert Spaces with Uniform Sampling [C] . Akira Tanaka IEEE International Conference on Acoustics, Speech and Signal Processing . 2018

机译：内核诱导翻译不变再现内核的采样定理与统一采样的核心核
5. ESTIMATES FOR REPRODUCING KERNELS IN WEIGHTED HILBERT SPACES OF ENTIRE FUNCTIONS. [D] . HANTLER, SIDNEY LAWRENCE. 1974

机译：在整个函数的加权希尔伯特空间中重现内核的估计。
6. Structured functional additive regression in reproducing kernel Hilbert spaces [O] . Hongxiao Zhu, Fang Yao, Hao Helen Zhang -1

机译：再现内核希尔伯特空间中的结构化功能加性回归
7. HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL [O] . García A.G, Hernández-Medina M.A, Portal A 2016

机译：解析希尔伯特-空间值核诱导的整函数的希尔伯特空间中翻译算子的超循环
8. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space [R] . Rosipal, R., Trejo, L. J. 2001

机译：再生核Hilbert空间中的核偏最小二乘回归

HYPERCYCLICITY OF TRANSLATION OPERATORS IN A REPRODUCING KERNEL HILBERT SPACE OF ENTIRE FUNCTIONS INDUCED BY AN ANALYTIC HILBERT-SPACE-VALUED KERNEL

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