We prove several Paley–Wiener-type theorems related to the spherical transform on the Gelfand pair H_n xU(n), U(n) , where H_n is the 2n + 1-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in R^2, we prove that spherical transforms of U(n)-invariant functions and distributions with compact support in H_n admit unique entire extensions to C^2 , and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations.

Paley–Wiener theorems for the U(n)-spherical transform on the Heisenberg group

ASTENGO, FRANCESCA;
2015

Abstract

We prove several Paley–Wiener-type theorems related to the spherical transform on the Gelfand pair H_n xU(n), U(n) , where H_n is the 2n + 1-dimensional Heisenberg group. Adopting the standard realization of the Gelfand spectrum as the Heisenberg fan in R^2, we prove that spherical transforms of U(n)-invariant functions and distributions with compact support in H_n admit unique entire extensions to C^2 , and we find real-variable characterizations of such transforms. Next, we characterize the inverse spherical transforms of compactly supported functions and distributions on the fan, giving analogous characterizations.
File in questo prodotto:
File Dimensione Formato  
Astengo2015_Article_PaleyWienerTheoremsForTheTextU.pdf

accesso chiuso

Tipologia: Documento in versione editoriale
Dimensione 554.11 kB
Formato Adobe PDF
554.11 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS 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: http://hdl.handle.net/11567/790008
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact