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Creators/Authors contains: "Levin, Eli"

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  1. ; (, Journal of Approximation Theory)
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  2. ; (, Journal of Spectral Theory)
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  3. (, Journal of approximation theory)
    We consider orthogonal polynomials {p_{n}(e^{-2nQ_{n}},x)} for varying measures and use universality limits to prove "local limits" lim_{n→∞}((p_{n}(e^{-2nQ_{n}},y_{jn}+(z/(K_{n}(y_{jn},y_{jn})))))/(p_{n}(e^{-2nQ_{n}},y_{jn})))e^{-((nQ_{n}′(y_{jn}))/(K_{n}(y_{jn},y_{jn})))z}=cosπz. Here y_{jn} is a local maximum point of |p_{n}|e^{-nQ_{n}} in the "bulk" of the support, K_{n}(y_{jn},y_{jn}) is the normalized reproducing kernel, and the limit holds uniformly for z in compact subsets of the plane. We also consider local limits at the "soft edge" of the spectrum, which involve the Airy function. 
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