The Fock Space in the Slice Hyperholomorphic Setting

The Fock Space in the Slice Hyperholomorphic Setting

Files

Link to Full Text

Download Full Text

Description

In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case of slice monogenic functions with values in a Clifford algebra. In the specific setting of quaternions, we also introduce the full Fock space. This paper can be seen as the beginning of the study of infinite dimensional analysis in the quaternionic setting.

ISBN

978-3-319-08771-9

Publication Date

2014

Publisher

Springer

City

Basel, Switzerland

Disciplines

Algebra | Discrete Mathematics and Combinatorics | Other Mathematics

Comments

This is a pre-copy-editing, author-produced PDF of a chapter accepted for publication in Hypercomplex Analysis: New perspectives and applications Trends in Mathematics, edited by S. Bernstein, U. Kähler, Irene Sabadini, and F. Sommen.

Copyright

Springer

The Fock Space in the Slice Hyperholomorphic Setting

Share

COinS