- journal article metadata
European Mathematical Society Publishing House
2018-02-09 23:30:02
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
34
2018
1
Composition operators on the Schwartz space
Antonio
Galbis
Universitat de València, Burjassot (València), Spain
Enrique
Jordá
Universitat Politècnica de València, Alcoy (Alicante), Spain
Composition operator, composite function problem, space of rapidly decreasing functions
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.
Operator theory
Functional analysis
397
412
10.4171/RMI/989
http://www.ems-ph.org/doi/10.4171/RMI/989
2
6
2018