The quaternionic Hardy space of slice regular functions H^2(B) is a reproducing kernel Hilbert space. In this note we see how this property can be exploited to construct a Riemannian metric on the quaternionic unit ball B and we study the geometry arising from this construction. We also show that, in contrast with the example of the Poincaré metric on the complex unit disc, no Riemannian metric on B is invariant with respect to all slice regular bijective self maps of B.

The quaternionic Hardy space and the geometry of the unit ball / Sarfatti, Giulia. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - ELETTRONICO. - (2015), pp. 103-115.

The quaternionic Hardy space and the geometry of the unit ball

SARFATTI, GIULIA
2015-01-01

Abstract

The quaternionic Hardy space of slice regular functions H^2(B) is a reproducing kernel Hilbert space. In this note we see how this property can be exploited to construct a Riemannian metric on the quaternionic unit ball B and we study the geometry arising from this construction. We also show that, in contrast with the example of the Poincaré metric on the complex unit disc, no Riemannian metric on B is invariant with respect to all slice regular bijective self maps of B.
2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/272343
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