Mathematics > Complex Variables
[Submitted on 21 Dec 2018 (v1), last revised 25 Aug 2019 (this version, v3)]
Title:S--polyregular Bargmann spaces
View PDFAbstract:We introduce two classes of right quaternionic Hilbert spaces in the context of slice polyregular functions, generalizing the so-called slice and full hyperholomorphic Bargmann spaces. Their basic properties are discussed, the explicit formulas of their reproducing kernels are given and associated Segal--Bargmann transforms are also introduced and studied. The spectral description as special subspaces of $L^2$-eigenspaces of a second order differential operator involving the slice derivative is investigated.
Submission history
From: Allal Ghanmi [view email][v1] Fri, 21 Dec 2018 14:11:29 UTC (24 KB)
[v2] Sat, 27 Jul 2019 00:27:04 UTC (26 KB)
[v3] Sun, 25 Aug 2019 20:30:19 UTC (27 KB)
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