## Communications in Mathematical Analysis

### Poly-Bergman Type Spaces on the Siegel Domain

#### 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 $\lambda>-1$.

#### Article information

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

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.cma/1356039036

Mathematical Reviews number (MathSciNet)
MR3011524

Zentralblatt MATH identifier
1262.32005

Subjects
Primary: 32A36
Secondary: 30H20: Bergman spaces, Fock spaces

#### Citation

Ramírez Ortega, Josué; Sánchez Nungaray, Armando. Poly-Bergman Type Spaces on the Siegel Domain. Commun. Math. Anal. 14 (2013), no. 2, 113--128. https://projecteuclid.org/euclid.cma/1356039036