Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

• Boiti, Chiara ^[3] ; Jornet, David ^[1] ; Oliaro, Alessandro ^[4] ; Schindl, Gerhard ^[2]
  1. [1] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
  2. [2] University of Vienna

     University of Vienna

     Innere Stadt, Austria

     
  3. [3] Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli n. 30, 44121, Ferrara, Italy
  4. [4] Dipartimento di Matematica, Università di Torino, Via Carlo Alberto n. 10, 10123, Torino, Italy

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 423-442
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We use techniques from time-frequency analysis to show that the space {\mathcal{S}}_\omega of rapidly decreasing \omega-ultradifferentiable functions is nuclear for every weight function \omega (t)=o(t) as t tends to infinity. Moreover, we prove that, for a sequence (M_p)_p satisfying the classical condition (M1) of Komatsu, the space of Beurling type {\mathcal{S}}_{(M_p)} when defined with L^{2} norms is nuclear exactly when condition (M2)' of Komatsu holds.