Revista Matemática Iberoamericana

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Volume 34, Issue 1, 2018, pp. 397–412
DOI: 10.4171/RMI/989

Published online: 2018-02-06

Composition operators on the Schwartz space

Antonio Galbis[1] and Enrique Jordá[2]

(1) Universitat de València, Burjassot (València), Spain
(2) Universitat Politècnica de València, Alcoy (Alicante), Spain

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.

Keywords: Composition operator, composite function problem, space of rapidly decreasing functions

Galbis Antonio, Jordá Enrique: Composition operators on the Schwartz space. Rev. Mat. Iberoam. 34 (2018), 397-412. doi: 10.4171/RMI/989