Abdelhamid Boussejra, Zouhaїr Mouyan, “A new formula for Berezin transforms attached to generalized Bergman spaces on the unit ball <nobr>$\mathbb B^n$</nobr>”, Mosc. Math. J., 2016, Volume 16, Number 4,Pages <nobr>641

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A new formula for Berezin transforms attached to generalized Bergman spaces on the unit ball $\mathbb B^n$

Abdelhamid Boussejra^a, Zouhaїr Mouyan^b

^a Department of Mathematics, Faculty of Sciences, Ibn Tofail University, PO Box. 133, Kénitra, Morocco
^b Department of Mathematics, Faculty of Sciences & Technics (M'Ghila), PO Box. 523, Béni Mellal, Morocco

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

Key words and phrases: пeneralized Bergman spaces, Berezin transforms, magnetic Schrödinger operator, Laplace–Beltrami operator, Fourier–Helgason transform.

MSC: 43A32, 47B35, 47G10, 81Q35

Received: September 1, 2014; in revised form February 8, 2016

Language: English

DOI: 10.17323/1609-4514-2016-16-4-641-649