Boolean convolution in the quaternionic setting

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• 作者：Daniel Alpay^a ; ^{dany@math.bgu.ac.il" class="auth_mail" title="E-mail the corresponding author} ; Marek Bożejko^b ; ^{bozejko@math.uni.wroc.pl" class="auth_mail" title="E-mail the corresponding author} ; Fabrizio Colombo^c ; ^{fabrizio.colombo@polimi.it" class="auth_mail" title="E-mail the corresponding author} ; David P. Kimsey^d ; ^{david.kimsey@ncl.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Irene Sabadini^c ; ^{irene.sabadini@polimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：46L51 ; 46L53 ; 47A57
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：506
• 期：Complete
• 页码：382-412
• 全文大小：451 K

文摘

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.