Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators

Details Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators

2012-04-04

arxiv.org/abs/1204.1033v2

Physics

Mathematical Physics

36 pages, many details clarified

Scientific paper

Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space and 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. Toeplitz operators are then defined using the reproducing kernel in the usual way, and some of their properties are proved. These quantum spaces provide non-trivial examples of spaces which have a reproducing kernel but are not spaces of functions.

Affiliated with

Also associated with

No associations

Rating

Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Paragrassmann Algebras are Quantum Spaces having Reproducing Kernels and Toeplitz Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-32875