Poly-Bergman Type Spaces on the Siegel Domain: Quasi-parabolic Case

Carlos Gonzalez-Flores, Josue Ramirez, Armando Sanchez Nungaray

Abstract


We introduce poly-Bergman type spaces on the Siegel domain $D_n\subset \mathbb{C}^n$, and we prove that they are isomorphic to tensorial products of one-dimensional spaces generated by orthogonal polynomials of two kinds: Laguerre polynomials and Hermite type polynomials. The linear span of all poly-Bergman type spaces is dense in the Hilbert space $L^2(D_n,d\mu_{\lambda})$, where $d\mu_{\lambda}=(\im z_n - |z_1|^2-\cdots -|z_{n-1}|^2)^{\lambda}dx_1dy_1\cdots dx_n dy_n$, with $\lambda>-1$.

Full Text: PDF DOI: 10.5539/jmr.v4n6p53

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This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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