Communications in Mathematical Physics - Volume 302 - download pdf or read online

By M. Aizenman (Chief Editor)

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A. Rakhmanov3 1 Department of Statistics and Applied Mathematics, University of Almería, 04120 Almeria, Spain. es 2 Instituto Carlos I de Física Teórica y Computacional, Granada University, 18071 Granada, Spain 3 Department of Mathematics, University of South Florida, Tampa, FL 33620, USA. edu Received: 6 April 2009 / Accepted: 25 July 2010 Published online: 8 January 2011 – © Springer-Verlag 2011 Abstract: We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials – polynomial solutions of second order differential equations with complex polynomial coefficients.

9. General Families of A-Critical Measures . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 56 59 64 67 81 87 90 101 108 54 A. Martínez-Finkelshtein, E. A. Rakhmanov 1. Generalized Lamé Equation Let us start with a classical problem more than 125 years old. Given a set of pairwise distinct points fixed on the complex plane C, A = {a0 , a1 , . . 3) where Vn is a polynomial (in general, depending on n) of degree ≤ p − 1; if deg V = p − 1, then V is monic.

Generalized Lamé Equation Let us start with a classical problem more than 125 years old. Given a set of pairwise distinct points fixed on the complex plane C, A = {a0 , a1 , . . 3) where Vn is a polynomial (in general, depending on n) of degree ≤ p − 1; if deg V = p − 1, then V is monic. 4) where Vn ∈ P p−1 is the “spectral polynomial”. Special instances of Eq. 3) are well known. For instance, p = 1 corresponds to the hypergeometric differential equation. g. [100, Ch. 23]). For the general situation of p = 2 we get Heun’s equation, which still attracts interest and poses open questions (see [76]).

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Communications in Mathematical Physics - Volume 302 by M. Aizenman (Chief Editor)


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