Polar Bergman Polynomials on Domain with Corners.

In this paper we present a new class named polar of monic orthogonal polynomials with respect to the area measure supported on G where G is a bounded simply-connected domain in the complex plane ℂ. We analyze some open questions and discuss some ideas properties related to solving asymptotic behavior of polar Bergman polynomials over domains with corners and asymptotic behavior of modified Bergman polynomials by affine transforms in variable and polar modified Bergman polynomials by affine transforms in variable. We show that uniform asymptotic of Bergman polynomials over domains with corners and by Pritsker's theorem imply uniform asymptotic for all their derivatives. [ABSTRACT FROM AUTHOR]