Document Type
Article
Publication Date
5-7-2021
Abstract
Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic X-ray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford-Krein modules are naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products for duality and topology, we are going to demonstrate how one can work with them Taking into account possible applications and the nature of hypercomplex analysis, special attention will be given to the study of Clifford-Krein modules with reproducing kernels. In the end we will discuss the interpolation problem in Clifford-Krein modules with reproducing kernel.
Recommended Citation
Alpay, D., Cerejeiras, P. & Kähler, U. Krein Reproducing Kernel Modules in Clifford Analysis. Journal d'Analyse Mathématique (2021). https://doi.org/10.1007/s11854-021-0155-6
Peer Reviewed
1
Copyright
Springer
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal d'Analyse Mathématique in 2021 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s11854-021-0155-6.
A free-to-read copy of the final published article is available here.