Choquet order for spectra of higher Lame operators and orthogonal polynomials

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We establish a hierarchy of weighted majorization relations for the singularities of generalized Lamé equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher Lamé operators. These relations translate into natural dilation and subordination properties in the Choquet order for certain probability measures associated with the aforementioned polynomials. As a consequence we obtain new inequalities for the moments and logarithmic potentials of the corresponding root-counting measures and their weak-$^*$ limits in the semi-classical and various thermodynamic asymptotic regimes. We also prove analogous results for systems of orthogonal polynomials such as Jacobi polynomials.
final version, to appear in J. Approx. Theory; 14 pages, no figures, LaTeX2e

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Classical Analysis and ODEs, Complex Variables, Spectral Theory, Primary 34L20; Secondary 30C15, 33C45, 60E15

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http://salesiana.dossiersoluciones.com/handle/123456789/158441

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702220
 http://arxiv.org/abs/math/0702220
 J. Approx. Theory 151 (2008), 164--180

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arXiv