About: On Spectral Polynomials of the Heun Equation. II

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. 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. (en)
Title	On Spectral Polynomials of the Heun Equation. II On Spectral Polynomials of the Heun Equation. II (en)
skos:prefLabel	On Spectral Polynomials of the Heun Equation. II On Spectral Polynomials of the Heun Equation. II (en)
skos:notation	RIV/61389005:_____/12:00384816!RIV13-AV0-61389005
http://linked.open...avai/predkladatel	Ústav jaderné fyziky AV ČR, v.v.i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(LC06002)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Tater, Miloš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	156338
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/12:00384816
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Heun equation; Van Vleck and Stieltjes polynomials; generalized canonical commutation relations; quadratic differential (en)
http://linked.open.../riv/klicoveSlovo	Heun equation Van Vleck and Stieltjes polynomials quadratic differential generalized canonical commutation relations
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[34DA52AE9FCC]
http://linked.open...i/riv/nazevZdroje	Communications in Mathematical Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	311
http://linked.open...iv/tvurceVysledku	Tater, Miloš Shapiro, B. Takemura, K.
http://linked.open...ain/vavai/riv/wos	000302243700001
issn	0010-3616
number of pages	24 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00220-012-1466-3
is http://linked.open...avai/riv/vysledek of	On Spectral Polynomials of the Heun Equation. II

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