Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness

Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness

We study the Hermite operator H=−Δ+|x|2 in Rd and its fractional powers Hβ, β>0 in phase space. Namely, we represent functions f via the so-called short-time Fourier, alias Fourier-Wigner or Bargmann transform Vgf (g being a fixed window function), and we measure their regularity and decay by mea...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Advances in mathematics (New York. 1965) 2021-12, Vol.392, p.107995, Article 107995
Hauptverfasser: Bhimani, Divyang G., Manna, Ramesh, Nicola, Fabio, Thangavelu, Sundaram, Trapasso, S. Ivan
Format: Artikel
Sprache:eng
Schlagworte:
Heat semigroup
Hermite operator
Modulation spaces
Nonlinear heat equation
Pseudodifferential operators
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study the Hermite operator H=−Δ+|x|2 in Rd and its fractional powers Hβ, β>0 in phase space. Namely, we represent functions f via the so-called short-time Fourier, alias Fourier-Wigner or Bargmann transform Vgf (g being a fixed window function), and we measure their regularity and decay by means of mixed Lebesgue norms in phase space of Vgf, that is in terms of membership to modulation spaces Mp,q, 0
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2021.107995