In this paper, we study Hankel operators in the quaternionic setting. In particular, we prove that they can be exploited to measure the L^\infty distance of a slice L^\infty function (i.e., an essentially bounded function on the quaternionic unit sphere that is affine with respect to quaternionic imaginary units) from the space of bounded slice regular functions (i.e., bounded quaternionic power series on the quaternionic unit ball). Among the difficulties arising from the non-commutative context, there is the lack of a good factorization result for slice regular functions in the Hardy space H^1

Quaternionic Hankel operators and approximation by slice regular functions / Sarfatti, Giulia. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 65:(2016), pp. 1735-1757. [10.1512/iumj.2016.65.5896]

Quaternionic Hankel operators and approximation by slice regular functions

SARFATTI, GIULIA
2016

Abstract

In this paper, we study Hankel operators in the quaternionic setting. In particular, we prove that they can be exploited to measure the L^\infty distance of a slice L^\infty function (i.e., an essentially bounded function on the quaternionic unit sphere that is affine with respect to quaternionic imaginary units) from the space of bounded slice regular functions (i.e., bounded quaternionic power series on the quaternionic unit ball). Among the difficulties arising from the non-commutative context, there is the lack of a good factorization result for slice regular functions in the Hardy space H^1
2016
65
1735
1757
Sarfatti, Giulia
File in questo prodotto:
File Dimensione Formato  
Pubblicazione_9_IUMJ.pdf

Accesso chiuso

Descrizione: articolo
Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 287.03 kB
Formato Adobe PDF
287.03 kB Adobe PDF   Richiedi una copia

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

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1062753
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 2
social impact