Title: ПРАВИЛА ОФОРМЛЕНИЯ ТЕЗИСОВ КОНФЕРЕНЦИИ ВНКСФ-7
Author: Sergey Trapeznikov
Last saved by: Psixej
Company: Saint-Petersburg State University

Direction: 010700 Physics 
Program: 28 Theory of elementary particles interaction and quantum field theory 
Department of High Energy and Elementary Particles Physics 
Scientific advisor: prof. V.D. Lyakhovsky 
Referee: associate prof. V.V. Borzov

Chebyshev basis for Hilbert space of smooth functions on Cartan subalgebra of simple Lie algebra
F.V. Uvarov

Polynomial constructions connected with solutions of problems of harmonic analysis on compact Riemannian symmetric space were studied as a probable bases for some Hilbert space. Different results on orthogonal polynomials associated with root systems were gathered and analyzed, and that allows the author to formulate some universal algorithms for multivariate Chebyshev polynomials and generalized Jacobi polynomials. We put our attention mostly on Chebyshev basis since it refers us to such well-known objects as characters and orbits of irreducible representations of simple Lie algebra.