The fock space in the slice hyperholomorphic setting

Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Guy Salomon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

38 Scopus citations

Abstract

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 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 infinitedimensional analysis in the quaternionic setting.

Original languageEnglish
Title of host publicationHypercomplex Analysis
Subtitle of host publicationNew Perspectives and Applications
EditorsSwanhild Bernstein, Uwe Kähler, Irene Sabadini, Frank Sommen
PublisherSpringer International Publishing
Pages43-59
Number of pages17
ISBN (Print)9783319087702
DOIs
StatePublished - 1 Jan 2014
Event9th International ISAAC Congress on International Society for Analysis, its Applications, and Computations, 2013 - Krakow, Poland
Duration: 5 Aug 20139 Aug 2013

Publication series

NameTrends in Mathematics
Volume65
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

Conference9th International ISAAC Congress on International Society for Analysis, its Applications, and Computations, 2013
Country/TerritoryPoland
CityKrakow
Period5/08/139/08/13

Keywords

  • Clifford algebras
  • Fock space
  • Quaternions
  • Slice hyperholomorphic functions

ASJC Scopus subject areas

  • Mathematics (all)

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