Počet záznamů: 1

On spectral polynomials of the Heun equation. I

  1. 1.
    0343020 - UJF-V 2011 RIV US eng J - Článek v odborném periodiku
    Shapiro, B. - Tater, Miloš
    On spectral polynomials of the Heun equation. I.
    Journal of Approximation Theory. Roč. 162, č. 4 (2010), s. 766-781 ISSN 0021-9045
    Grant CEP: GA MŠk LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: Heun equation * Spectral polynomials * Asymptotic root distribution
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 0.710, rok: 2010

    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.
    Trvalý link: http://hdl.handle.net/11104/0185599