Moscow Mathematical Journal

Volume 16, Issue 4, October–December 2016 pp. 641–649.

A New Formula for Berezin Transforms Attached to Generalized Bergman Spaces on the Unit Ball 𝔹ⁿ

Authors: Abdelhamid Boussejra (1) and Zouhaïr Mouayn (2)
Author institution:(1) Department of Mathematics, Faculty of Sciences, Ibn Tofail University, PO Box. 133, Kénitra, Morocco.
(2) Department of Mathematics, Faculty of Sciences & Technics (M'Ghila), PO Box. 523, Béni Mellal, Morocco.

Summary:

To each generalized Bergman space on the unit ball a Berezin transform is attached. We add a new formula representing this transform as a function of the Laplace–Beltrami operator by using the Fourier–Helgason transform.

2010 Math. Subj. Class. 43A32, 47B35, 47G10, 81Q35.

Keywords: Generalized Bergman spaces, Berezin transforms, magnetic Schrödinger operator, Laplace–Beltrami operator, Fourier–Helgason transform.

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