Quaternionic Fock space on slice hyperholomorphic functions

2016/11/16 by Kumar, Sanjay, Sharma, S. D., Manzoor, Khalid
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1611.05199

Abstract

In this paper, we define the quaternionic Fock spaces \mathfrakF_α^p of entire slice hyperholomorphic functions in a quaternionic unit ball \mathbbB in ℍ. We also study growth estimate and various results of entire slice regular functions in these spaces. The work of this paper is motivated by the recent work of \citealpa12 and \citemarco.

Related

• The Fock space in the slice hyperholomorphic setting
• A connection between quaternionic slice regular and Fueter hyperholormorphic functions
• BMO- and VMO-spaces of slice hyperholomorphic functions
• A quaternionic analogue of the Segal-Bargmann transform
• Quaternionic Fock space in an Euclidean unit ball \mathbbBⁿ