Convex characteristics of quaternionic positive definite functions on abelian groups

DOI10.1007/s00006-024-01336-9MaRDI QIDQ6577781

Jing Ning Liu, Zeping Zhu

Publication date: 24 July 2024

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

zbMATH Keywords

abelian grouppositive definite functionquaternionBauer simplexFourier-type transform

Mathematics Subject Classification ID

Other transforms and operators of Fourier type (43A32) Convex sets in topological linear spaces; Choquet theory (46A55) Positive definite functions on groups, semigroups, etc. (43A35) Character groups and dual objects (43A40) Quaternionic functional analysis (46S05)

Cites Work

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• An extension of Herglotz's theorem to the quaternions
• The \(H^{\infty}\) functional calculus based on the \(S\)-spectrum for quaternionic operators and for \(n\)-tuples of noncommuting operators
• Exponentially bounded positive definite functions
• Positive definite functions on Abelian semigroups
• Quaternion-valued positive definite functions on locally compact abelian groups and nuclear spaces
• Positive-definite functions on involution semigroups
• The spectral theorem for quaternionic unbounded normal operators based on the \(S\)-spectrum
• On a class of quaternionic positive definite functions and their derivatives
• Natural structures on semigroups with involution
• Normal Operators on Quaternionic Hilbert Spaces

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