We study the initial value problem for Schr"odinger-type equations with initial data presenting a certain Gevrey regularity and an exponential behavior at infinity. We assume the lower order terms of the Schrödinger operator depending on (t,x) in [0,T]xR^n and complex valued. Under a suitable decay condition as |x| goes to infinity on the imaginary part of the first order term and an algebraic growth assumption on the real part, we derive global energy estimates in suitable Sobolev spaces of infinite order and prove a well posedness result in Gelfand-Shilov type spaces. We also discuss by examples the sharpness of the result.

Schrödinger-type equations in Gelfand-Shilov spaces

Alessia Ascanelli;Marco Cappiello
2019

Abstract

We study the initial value problem for Schr"odinger-type equations with initial data presenting a certain Gevrey regularity and an exponential behavior at infinity. We assume the lower order terms of the Schrödinger operator depending on (t,x) in [0,T]xR^n and complex valued. Under a suitable decay condition as |x| goes to infinity on the imaginary part of the first order term and an algebraic growth assumption on the real part, we derive global energy estimates in suitable Sobolev spaces of infinite order and prove a well posedness result in Gelfand-Shilov type spaces. We also discuss by examples the sharpness of the result.
2019
Ascanelli, Alessia; Cappiello, Marco
File in questo prodotto:
File Dimensione Formato  
AscanelliCapielloJMPA_finalpublished.pdf

solo gestori archivio

Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 745.42 kB
Formato Adobe PDF
745.42 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1807.04571.pdf

accesso aperto

Tipologia: Pre-print
Licenza: Creative commons
Dimensione 532.42 kB
Formato Adobe PDF
532.42 kB Adobe PDF Visualizza/Apri

I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2402994
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 10
social impact