Fine Asymptotics for Bergman Polynomials over Domains with Corners
نویسندگان
چکیده
Let G be a bounded simply-connected domain in the complex plane C, whose boundary Γ := ∂G is a Jordan curve, and let {pn} ∞ n=0 denote the sequence of Bergman polynomials of G. This is defined as the sequence pn(z) = λnz n + · · · , λn > 0, n = 0, 1, 2, . . . , of polynomials that are orthonormal with respect to the inner product
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Boundary Estimates for Bergman Polynomials in Domains with Corners
Let G be a bounded simply-connected domain in the complex plane C, whose boundary Γ := ∂G is a Jordan curve, and let {pn}n=0 denote the sequence of Bergman polynomials of G. This is defined as the unique sequence of polynomials {pn(z)}n=0, with positive leading coefficient, that are orthonormal with respect to the area measure on G. The asymptotic behaviour of pn(z) in the exterior of Γ, in cas...
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