Representation of moduli spaces of curves and calculation of extremal polynomials

Journal Article · Wed Apr 30 00:00:00 EDT 2003 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2003V194N04ABEH000725; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21208309

Bogatyrev, A B ^[1]

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1. Institute of Computational Mathematics of the Russian Academy of Sciences, Moscow (Russian Federation)

The classical Chebyshev and Zolotarev polynomials are the first ranks of the hierarchy of extremal polynomials, which are typical solutions of problems on the conditional minimization of the uniform norm over a space of polynomials. In the general case such polynomials are connected with hyperelliptic curves the genus of which labels the ranks of the hierarchy. Representations of the moduli spaces of such curves are considered in this paper with applications to the calculation of extremal polynomials. Uniformizing curves by special Schottky groups one obtains effectively computable parametric expressions for extremal polynomials in terms of linear series of Poincare.

• OSTI ID: 21208309
• Journal Information: Sbornik. Mathematics, Vol. 194, Issue 4; Other Information: DOI: 10.1070/SM2003v194n04ABEH000725; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MINIMIZATION
POLYNOMIALS