Linear Factorization of Hypercyclic Functions for Differential Operators

2019/12/05 by Chan, Kit C., Hofstad, Jakob, Walmsley, David
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.02371

Abstract

On the Fréchet space of entire functions H(ℂ), we show that every nonscalar continuous linear operator L:H(ℂ)→ H(ℂ) which commutes with differentiation has a hypercyclic vector f(z) in the form of the infinite product of linear polynomials: f(z) = ∏_j=1^∞ ( 1-(z)/(a_j)), where each a_j is a nonzero complex number.

Related

• Existence of common hypercyclic subspaces for the derivative operator\n and the translation operators
• Typicality of operators on Fréchet algebras admitting a hypercyclic algebra
• Hypercyclic differentiation operators
• Common hypercyclic vectors for certain families of differential operators
• A review of some recent work on hypercyclicity