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

Carlos Gonzalez-Flores, Josue Ramirez, Armando Sanchez Nungaray


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:


DOI: http://dx.doi.org/10.5539/jmr.v4n6p53

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

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.