On Spectral Polynomials of the Heun Equation. II

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F12%3A00384816" target="_blank" >RIV/61389005:_____/12:00384816 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00220-012-1466-3" target="_blank" >http://dx.doi.org/10.1007/s00220-012-1466-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00220-012-1466-3" target="_blank" >10.1007/s00220-012-1466-3</a>

Result language
angličtina
Original language name
On Spectral Polynomials of the Heun Equation. II
Original language description
The well-known Heun equation has the form {Q(z)d(2)/dz(2) + P(z)d/dz + V(z)} S(z) = 0, where Q(z) is a cubic complex polynomial, P(z) and V(z) are polynomials of degree at most 2 and 1 respectively. One of the classical problems about the Heun equation suggested by E. Heine and T. Stieltjes in the late 19th century is for a given positive integer n to find all possible polynomials V(z) such that the above equation has a polynomial solution S(z) of degree n. Below we prove a conjecture of the second author, see Shapiro and Tater (JAT 162: 766-781, 2010) claiming that the union of the roots of such V(z)'s for a given n tends when n. 8 to a certain compact connecting the three roots of Q(z) which is given by a condition that a certain natural abelian integral is real-valued, see Theorem 2. In particular, we prove several new results of independent interest about rational Strebel differentials.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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