Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures |
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Authors: | D. Barrios Rolaní a, B. de la Calle Ysern,G. L pez Lagomasino |
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Affiliation: | aFacultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, 28660 Boadilla del Monte, Madrid, Spain;bETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José G. Abascal 2, 28006 Madrid, Spain;cDpto. de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad 15, 28911 Leganés, Madrid, Spain |
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Abstract: | Let μ be a finite positive Borel measure with compact support consisting of an interval plus a set of isolated points in , such that μ′>0 almost everywhere on [c,d]. Let , be a sequence of polynomials, , with real coefficients whose zeros lie outside the smallest interval containing the support of μ. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form dμ/w2n. In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above. |
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Keywords: | Varying measures Ratio asymptotics Relative asymptotics Nikishin system Hermite– Padé orthogonal polynomials |
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