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dc.contributor.authorMartínez-Finkelshtein, Andrei
dc.contributor.authorRakhmanov, Evgenii A.
dc.date.accessioned2012-08-01T08:01:46Z
dc.date.available2012-08-01T08:01:46Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/10835/1628
dc.description.abstractWe investigate the asymptotic zero distribution of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. In the case when all zeros of the leading coefficients are all real, zeros of the Heine-Stieltjes polynomials were interpreted by Stieltjes as discrete distributions minimizing an energy functional. In a general complex situation one deals instead with a critical point of the energy. We introduce the notion of discrete and continuous critical measures (saddle points of the weighted logarithmic energy on the plane), and prove that a weak-* limit of a sequence of discrete critical measures is a continuous critical measure. Thus, the limit zero distributions of the Heine-Stieltjes polynomials are given by continuous critical measures. We give a detailed description of such measures, showing their connections with quadratic differentials. In doing that, we obtain some results on the global structure of rational quadratic differentials on the Riemann sphere that have an independent interest.es_ES
dc.language.isoenes_ES
dc.sourceCommunications in Mathematical Physics Volume 302, Number 1 (2011)es_ES
dc.subjectDistribución asintótica a ceroes_ES
dc.subjectPolinomios de Heine-Stieltjeses_ES
dc.subjectEcuaciones diferencialeses_ES
dc.subjectCoeficientes polinomiales complejoses_ES
dc.subjectAsymptotic zero distributiones_ES
dc.subjectHeine-Stieltjes polynomialses_ES
dc.subjectDifferential equationses_ES
dc.subjectComplex polynomial coefficientses_ES
dc.titleCritical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomialses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses_ES


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