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2013 Poly-Bergman Type Spaces on the Siegel Domain
Josué Ramírez Ortega, Armando Sánchez Nungaray
Commun. Math. Anal. 14(2): 113-128 (2013).

Abstract

We introduce poly-Bergman type spaces on the Siegel domain $D_n\subset \mathbb{C}^n$, 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 $L^2(D_n,d\mu_{\lambda})$, where $d\mu_{\lambda}=(\mathrm{Im}\, z_n |z_1|^2-\cdots -|z_{n-1}|^2)^{\lambda}dx_1dy_1\cdots dx_n dy_n$ and $\lambda>-1$.

Citation

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Josué Ramírez Ortega. Armando Sánchez Nungaray. "Poly-Bergman Type Spaces on the Siegel Domain." Commun. Math. Anal. 14 (2) 113 - 128, 2013.

Information

Published: 2013
First available in Project Euclid: 20 December 2012

zbMATH: 1262.32005
MathSciNet: MR3011524

Subjects:
Primary: ‎32A36‎
Secondary: 30H20

Keywords: Bergman spaces , Polyanalytic functions , Siegel domain

Rights: Copyright © 2013 Mathematical Research Publishers

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Vol.14 • No. 2 • 2013
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