The Szeg "o metric associated to Hardy spaces of Clifford algebra valued\n functions and some geometric properties

2011/03/16 by Dennis Grob, Grob, Dennis, Rolf Soeren Krausshar +1
Mathematics · #30G35 #32A25 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1103.3195

openalex publication_date 2011/03/16 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In analogy to complex function theory we introduce a Szeg "o metric in the\ncontext of hypercomplex function theory dealing with functions that take values\nin a Clifford algebra. In particular, we are dealing with Clifford algebra\nvalued functions that are annihilated by the Euclidean Dirac operator in\n\ℝ^m+1. These are often called monogenic functions. As a\nconsequence of the isometry between two Hardy spaces of monogenic functions on\ndomains that are related to each other by a conformal map, the generalized\nSzeg "o metric turns out to have a pseudo-invariance under M "obius\ntransformations. This property is crucially applied to show that the curvature\nof this metric is always negative on bounded domains. Furthermore, it allows us\nto establish that this metric is complete on bounded domains.\n

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