Existence of common hypercyclic subspaces for the derivative operator\n and the translation operators

2016/11/25 by Quentin Menet, Menet, Quentin
Mathematics · #47A16 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1611.08564

openalex publication_date 2016/11/25 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

We show that the non-zero multiples of the derivative operator and the\nnon-zero multiples of non-trivial translation operators on the space of entire\nfunctions share a common hypercyclic subspace, i.e. a closed\ninfinite-dimensional subspace in which each non-zero vector has a dense orbit\nfor each of these operators.\n

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