Articulos FC INSMAT

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Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
(2024-04-03) Carlos Féliz Sánchez
Given a sequence of orthogonal polynomials {𝐿𝑛}∞𝑛=0, orthogonal with respect to a positive Borel 𝜈 measure supported on ℝ+, let {𝑄𝑛}∞𝑛=0 be the the sequence of orthogonal polynomials with respect to the modified measure 𝑟(𝑥)𝑑𝜈(𝑥), where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula 𝑄(𝑑)𝑛(𝑧)𝐿(𝑑)𝑛(𝑧)⇉𝑛∏𝑁1𝑘=1(𝑎𝑘√+𝑖𝑧√+𝑎𝑘√)𝐴𝑘∏𝑁2𝑗=1(𝑧√+𝑏𝑗√𝑏𝑗√+𝑖)𝐵𝑗, on compact subsets of ℂ∖ℝ+, where 𝑎𝑘 and 𝑏𝑗 are the zeros and poles of r, and the 𝐴𝑘, 𝐵𝑗 are their respective multiplicities.