M-harmonic reproducing kernels on the ball

0577235 - MÚ 2025 RIV NL eng J - Článek v odborném periodiku
Engliš, Miroslav - Youssfi, E.-H.
M-harmonic reproducing kernels on the ball.
Journal of Functional Analysis. Roč. 286, č. 1 (2024), č. článku 110187. ISSN 0022-1236. E-ISSN 1096-0783
Institucionální podpora: RVO:67985840
Klíčová slova: Bergman kernel * invariant Laplacian * M-harmonic function * Szegö kernel
Obor OECD: Pure mathematics
Impakt faktor: 1.7, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jfa.2023.110187

Using the machinery of unitary spherical harmonics due to Koornwinder, Folland and other authors, we obtain expansions for the Szegö and the weighted Bergman kernels of M-harmonic functions, i.e. functions annihilated by the invariant Laplacian on the unit ball of the complex n-space. This yields, among others, an explicit formula for the M-harmonic Szegö kernel in terms of multivariable as well as single-variable hypergeometric functions, and also shows that most likely there is no explicit (“closed”) formula for the corresponding weighted Bergman kernels.
Trvalý link: https://hdl.handle.net/11104/0346445