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Poly-Bergman Type Spaces on the Siegel Domain

Commun. Math. Anal.
Volume 14, Number 2 (2013), 113 - 128

Poly-Bergman Type Spaces on the Siegel Domain

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Abstract

We introduce poly-Bergman type spaces on the Siegel domain Dn Cn, and prove that they are isomorphic to tensor products of one-dimensional spaces generated by orthogonal polynomials of two kinds: Laguerre and Hermite polynomials. The linear span of all poly-Bergman type spaces is dense in the Hilbert space L2(Dn,dμλ), where dμλ = (Imzn −|z1|2 −∙∙∙−|zn−1|2)λdx1dy1 ∙∙∙dxndyn and λ > −1.