S--polyregular Bargmann spaces
Complex Variables
2019-08-27 v3
Abstract
We introduce two classes of right quaternionic Hilbert spaces in the context of slice polyregular functions, generalizing the so-called slice and full hyperholomorphic Bargmann spaces. Their basic properties are discussed, the explicit formulas of their reproducing kernels are given and associated Segal--Bargmann transforms are also introduced and studied. The spectral description as special subspaces of -eigenspaces of a second order differential operator involving the slice derivative is investigated.
Keywords
Cite
@article{arxiv.1812.09129,
title = {S--polyregular Bargmann spaces},
author = {Abdelhadi Benahmadi and Amal El Hamyani and Allal Ghanmi},
journal= {arXiv preprint arXiv:1812.09129},
year = {2019}
}
Comments
Improved version of arXiv:1707.01674. 26 pages. To appear in "Advances in Applied Clliford Algebras". arXiv admin note: text overlap with arXiv:1707.01674 by other authors