On spectral polynomials of the Heun equation. II

DOI10.1007/s00220-012-1466-3zbMath1266.34139arXiv0904.0650OpenAlexW2569262973MaRDI QIDQ2428488

Kouichi Takemura, Miloš Tater, Boris Zalmanovich Shapiro

Publication date: 26 April 2012

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.0650

zbMATH Keywords

Heun equationStrebel differentialsgeneralized Lamé equation

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Lamé, Mathieu, and spheroidal wave functions (33E10) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (13)

Combinatorial description of jumps in spectral networks defined by quadratic differentials ⋮ Root-counting Measures of Jacobi Polynomials and Topological Types and Critical Geodesics of Related Quadratic Differentials ⋮ On higher Heine-Stieltjes polynomials ⋮ Spectral asymptotics for Kac-Murdock-Szegő matrices ⋮ On spectral asymptotic of quasi-exactly solvable quartic potential ⋮ Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems ⋮ S-curves in polynomial external fields ⋮ On spectral polynomials of the Heun equation. I ⋮ On the distribution and interlacing of the zeros of Stieltjes polynomials ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ Phase transitions and equilibrium measures in random matrix models ⋮ Quadratic differentials and signed measures ⋮ On existence of quasi-Strebel structures for meromorphic \(k\)-differentials

Cites Work

• Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials
• On higher Heine-Stieltjes polynomials
• On polynomial eigenfunctions for a class of differential operators
• On spectral polynomials of the Heun equation. I
• The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
• Asymptotic properties of Heine--Stieltjes and Van Vleck polynomials.
• On the zeros of complex Van Vleck polynomials
• Analytic continuation of eigenvalues of the Lamé operator
• Root asymptotics of spectral polynomials for the Lamé operator
• Analytic capacity and measure
• Algebro-geometric aspects of Heine-Stieltjes theory
• On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
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