2012/04/04 by Stephen Bruce Sontz, Sontz, Stephen Bruce
Computer Science · Mathematics · Physics and Astronomy · #46E22 #81R05 #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1204.1033
openalex publication_date 2012/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have reproducing kernels. These algebras are not isomorphic to algebras of functions so some care must be taken in defining what "evaluation at a point" corresponds to in this context. The reproducing kernel in the Segal-Bargmann space is shown to have most, though not all, of the standard properties. These quantum spaces provide non-trivial examples of spaces which have a reproducing kernel but which are not spaces of functions.