Spectrum of composition operators on ${\mathcal S}({\mathbb R})$ with polynomial symbols

Carmen Fernández; Antonio Galbis; Enrique Jordá

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arXiv · 1810.13208

Spectrum of composition operators on ${\mathcal S}({\mathbb R})$ with polynomial symbols

Carmen Fernández·Antonio Galbis·Enrique Jordá

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Abstract

We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to 0, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origen. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.

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BibTeX RIS

Carmen Fernández, Antonio Galbis, Enrique Jordá. 2018-10-31. Spectrum of composition operators on ${\mathcal S}({\mathbb R})$ with polynomial symbols. https://arxiv.org/abs/1810.13208

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