arXiv:1511.03072 Abstract | arXiv Analytics

arXiv:1511.03072 [math.FA]Abstract References Reviews Resources

Composition operators on the Schwartz space

Published 2015-11-10Version 1

We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.

Categories: math.FA

Subjects: 47B33, 46F05, 47A05

Keywords: schwartz space, study composition operators, closed range property, schwartz class, compact operator

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