Composition operators on the Schwartz space

• Antonio Galbis ^[1] ; Enrique Jordá ^[2]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
  2. [2] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 1, 2018, págs. 397-412
• Idioma: inglés
• DOI: 10.4171/RMI/989
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.