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; Sarfatti, Giulia. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 25:(2015), pp. 2028-2059. [10.1007/s12220-014-9503-4]
Invariant metrics for the quaternionic Hardy space
SARFATTI, GIULIA
2015-01-01
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:
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