We find Riemannian metrics on the unit ball of the quaternions, which are naturally associated with reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex variable case, no Riemannian metric is invariant under all regular self-maps of the quaternionic ball.

Invariant metrics for the quaternionic Hardy space

ARCOZZI, NICOLA
2015

Abstract

We find Riemannian metrics on the unit ball of the quaternions, which are naturally associated with reproducing kernel Hilbert spaces. We study the metric arising from the Hardy space in detail. We show that, in contrast to the one-complex variable case, no Riemannian metric is invariant under all regular self-maps of the quaternionic ball.
File in questo prodotto:
File Dimensione Formato  
JGeomAnal25-2015.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 357.97 kB
Formato Adobe PDF
357.97 kB Adobe PDF Visualizza/Apri

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: https://hdl.handle.net/11585/548656
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 13
social impact