Coherent states quantization of generalized bergman spaces on the unit ball of cn with a new formula for their associated berezin transforms

2012/04/04 by A. Boussejra, Boussejra, A., Z. Mouayn +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.FA #math.MP

paper · pdf · doi:10.48550/arxiv.1204.0934

11 pages

arxiv created 2012/05/07 · arxiv updated 2012/05/08

Abstract

While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the Berezin transforms attached to these spaces. Finally, a new formula representing these transforms a functions of the Laplace-Beltrami operator is established in terms ofWilson polynomials by using the Fourier-Helgason transform.

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