On Spectral Polynomials of the Heun Equation. II

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On Spectral Polynomials of the Heun Equation. II

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Spectral Polynomials of the Heun Equation. II

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

<a href="/cs/project/LC06002" target="_blank" >LC06002: Dopplerův ústav pro matematickou fyziku a aplikovanou matematiku</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematical Physics

ISSN

0010-3616

e-ISSN

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Svazek periodika

311

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

24

Strana od-do

277-300

Kód UT WoS článku

000302243700001

EID výsledku v databázi Scopus

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