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Statements

Subject Item
n2:RIV%2F61389005%3A_____%2F10%3A00343020%21RIV11-MSM-61389005
rdf:type
skos:Concept n15:Vysledek
dcterms:description
The classical 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) is a polynomial of degree at most 2 and V(z) is at most linear. In the second half of the nineteenth century E. Heine and T. Stieltjes initiated the study of the set of all V(z) for which the above equation has a polynomial solution S(z) of a given degree n. The main goal of the present paper is to study the union of the roots of the latter set of V(z)'s when n -> infinity. We provide an explicit description of this limiting set and give a substantial amount of preliminary and additional information about it obtained using a certain technique developed by A.B.J. Kuijlaars and W. Van Assche. The classical 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) is a polynomial of degree at most 2 and V(z) is at most linear. In the second half of the nineteenth century E. Heine and T. Stieltjes initiated the study of the set of all V(z) for which the above equation has a polynomial solution S(z) of a given degree n. The main goal of the present paper is to study the union of the roots of the latter set of V(z)'s when n -> infinity. We provide an explicit description of this limiting set and give a substantial amount of preliminary and additional information about it obtained using a certain technique developed by A.B.J. Kuijlaars and W. Van Assche.
dcterms:title
On spectral polynomials of the Heun equation. I On spectral polynomials of the Heun equation. I
skos:prefLabel
On spectral polynomials of the Heun equation. I On spectral polynomials of the Heun equation. I
skos:notation
RIV/61389005:_____/10:00343020!RIV11-MSM-61389005
n3:aktivita
n8:P n8:Z
n3:aktivity
P(LC06002), Z(AV0Z10480505)
n3:cisloPeriodika
4
n3:dodaniDat
n16:2011
n3:domaciTvurceVysledku
n12:6147275
n3:druhVysledku
n9:J
n3:duvernostUdaju
n10:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
276808
n3:idVysledku
RIV/61389005:_____/10:00343020
n3:jazykVysledku
n17:eng
n3:klicovaSlova
Heun equation; Spectral polynomials; Asymptotic root distribution
n3:klicoveSlovo
n14:Spectral%20polynomials n14:Heun%20equation n14:Asymptotic%20root%20distribution
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[D0A04E111BB3]
n3:nazevZdroje
Journal of Approximation Theory
n3:obor
n6:BE
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n18:LC06002
n3:rokUplatneniVysledku
n16:2010
n3:svazekPeriodika
162
n3:tvurceVysledku
Shapiro, B. Tater, Miloš
n3:wos
000276696200009
n3:zamer
n7:AV0Z10480505
s:issn
0021-9045
s:numberOfPages
16