In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carathéodory and Herglotz functions.

Boolean convolution in the quaternionic setting

COLOMBO, FABRIZIO;SABADINI, IRENE MARIA
2016-01-01

Abstract

In this paper we begin a study of free analysis in the quaternionic setting, and consider Boolean convolution for quaternion-valued measures. To this end we also study Boolean convolution for matrix-valued complex measures, also proving Boolean infinite divisibility and central limit theorems for these measures. Moreover we prove an integral representation for quaternionic Carathéodory and Herglotz functions.
2016
Boolean convolution; Herglotz and Carathéodory functions; Matrix-valued measures; Quaternionic-valued measures; Algebra and Number Theory; Numerical Analysis; Geometry and Topology; Discrete Mathematics and Combinatorics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1007252
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