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<p>We answer the question posed in 2017 by Muro, Pinasco, and Savransky.Specifically, we show that some nonconvolution operators defined on the space of entire functions&#xa0;<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1548_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$ H(𝔺^{N}) $</EquationSource> </InlineEquation>, with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1548_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$ N&gt;1 $</EquationSource> </InlineEquation>, are frequently hypercyclic. These operators are of the following type: a&#xa0;differentiation operator composed with an affine endomorphism which acts asa&#xa0;translation in at least one of its variables.We&#xa0;thus complete the study of frequent hypercyclicity initiated by Muro and co-authors.</p>

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Frequent Hypercyclic Behavior of Some Nonconvolution Operators on \( H(𝔺^{N}) \)

  • 期刊论文

  • 发表日期：

    2025年3月23日

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  • A. Karapetyants,
  • F. León-Saavedra,
  • J. Salvador

摘要

We answer the question posed in 2017 by Muro, Pinasco, and Savransky.Specifically, we show that some nonconvolution operators defined on the space of entire functions  $ H(𝔺^{N}) $ , with $ N>1 $ , are frequently hypercyclic. These operators are of the following type: a differentiation operator composed with an affine endomorphism which acts asa translation in at least one of its variables.We thus complete the study of frequent hypercyclicity initiated by Muro and co-authors.