On a series representation for Carleman orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
On a Series Representation for Carleman Orthogonal Polynomials
Let {pn(z)}n=0 be a sequence of complex polynomials (pn of degree n) that are orthonormal with respect to the area measure over the interior domain of an analytic Jordan curve. We prove that each pn of sufficiently large degree has a primitive that can be expanded in a series of functions recursively generated by a couple of integral transforms whose kernels are defined in terms of the degree n...
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Abstract. In this paper we investigate the asymptotic behavior of polynomials that are orthonormal over the interior domain of an analytic Jordan curve L with respect to area measure. We prove that, inside L, these polynomials behave asymptotically like a sequence of certain integrals involving the canonical conformal map of the exterior of L onto the exterior of the unit circle and certain mer...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10583-x