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On Rational Functions Orthogonal to All Powers of a Given Rational Function on a Curve

2013
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Moscow Mathematical Journal
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In this paper we study the generating function f (t) for the sequence of the moments γ P i (z)q(z)dz, i 0, where P (z), q(z) are rational functions of one complex variable and γ is a curve in C. We calculate an analytical expression for f (t) and provide conditions implying that f (t) is rational or vanishes identically. In particular, for P (z) in generic position we give an explicit criterion for a function q(z) to be orthogonal to all powers of P (z) on γ. As an application, we prove a

doi:10.17323/1609-4514-2013-13-4-693-731
fatcat:7pjms4oeaffbxkc6auzilcy3dy