Orbits of semigroups of truncated convolution operators

Stanislav Shkarin

doi:10.1017/S0017089512000055

Orbits of semigroups of truncated convolution operators

Stanislav Shkarin

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Abstract

We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

Original language	English
Pages (from-to)	399-414
Number of pages	16
Journal	Glasgow Mathematical Journal
Volume	54
Early online date	29 Mar 2012
DOIs	https://doi.org/10.1017/S0017089512000055
Publication status	Published - May 2012

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title = "Orbits of semigroups of truncated convolution operators",

abstract = "We prove that a semigroup generated by finitely many truncated convolution operators on \$L\_p[0, 1]\$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.",

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AB - We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

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JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

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Orbits of semigroups of truncated convolution operators

Abstract

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