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About the Nuclearity of \(\mathcal {S}_{(M_{p})}\) and \(\mathcal {S}_{\omega }\)

  • Chiara BoitiEmail author
  • David Jornet
  • Alessandro Oliaro
Chapter
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Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We use an isomorphism established by Langenbruch between some sequence spaces and weighted spaces of generalized functions to give sufficient conditions for the (Beurling type) space \(\mathcal {S}_{(M_p)}\) to be nuclear. As a consequence, we obtain that for a weight function ω satisfying the mild condition: 2ω(t) ≤ ω(Ht) + H for some H > 1 and for all t ≥ 0, the space \(\mathcal {S}_\omega \) in the sense of Björck is also nuclear.

Keywords

Nuclear spaces Weighted spaces of ultradifferentiable functions of Beurling type 

Notes

Acknowledgements

We are grateful to Prof. Gerhard Schindl for pointing out that (M2) is equivalent to (3), under (M1).

The authors were partially supported by the Projects FAR 2017, FAR 2018 and FIR 2018 (University of Ferrara), FFABR 2017 (MIUR). The research of the second author was partially supported by the project MTM2016-76647-P. The first and third authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di FerraraFerraraItaly
  2. 2.Instituto Universitario de Matemática Pura y Aplicada IUMPAUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

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