منابع مشابه
On Higher Heine-stieltjes Polynomials
Take a linear ordinary differential operator d(z) = Pk i=1 Qi(z) d dzi with polynomial coefficients and set r = maxi=1,...,k(degQi(z) − i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a nondegenerate higher Lamé operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [6] the study of the following multiparameter spectral problem...
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We study the asymptotic behavior of the zeros of polynomial solutions of a class of generalized Lamé differential equations, when their coefficients satisfy certain asymptotic conditions. The limit distribution is described by an equilibrium measure in presence of an external field, generated by charges at the singular points of the equation. Moreover, a case of non-positive charges is consider...
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The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = Pk i=1Qi(z) d dzi with polynomial coefficients set r = maxi=1,...,k(degQi(z)− i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) degQk(z) = k + r we call it a non-degenerate higher Lamé operator. Following...
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The Heine–Stieltjes Theorem describes the polynomial solutions, (v, f) such that T (f) = vf , to specific second order differential operators, T , with polynomial coefficients. We extend the theorem to concern all (nondegenerate) differential operators preserving the property of having only real zeros, thus solving a conjecture of B. Shapiro. The new methods developed are used to describe intri...
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The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = P k i=1 Q i (z) d i dz i with polynomial coefficients set r = max i=1,...,k (deg Q i (z) − i). If d(z) satisfies the conditions: i) r ≥ 0 and ii) deg Q k (z) = k + r we call it a non-degenerate higher Lamé ope...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2011
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-011-0051-3