This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
On the characterization of Chebyshev systems and on conditions of their extension, Y.G. Abakumov; Chebyshev polynomials with multiple zeros, B. Bojanov; a new method for generating infinite sets of related sequences of orthogonal polynomials, starting from first-order initial-value problems, C.C. Grosjean; orthogonal polynomials on n-spheres - Gegenbauer, Jacobi and Heun, E.G. Kalnins and W. Miller, Jr.; on the completeness of orthogonal polynomials in left-definite Sobolex spaces, W.N. Everitt et al; extremal problems for polynomials and their coefficients, G.V. Milovanovic et al; new inequalities for polynomials functions, Th.M. Rassias; artificial intelligence today, G.C. Rota; a certain family of generating functions for classical orthogonal polynomials, H.M. Srivastava; mean number of real zeros of a random trigonometric polynomial, J.E. Wilkins, Jr.; orthogonal polynomials of many variables and degenerated elliptic equations, A. Yanushauskas; the convexity of Chebyshev sets in Hilbert space, F. Deutsch; on Lagrange polynomial quasi-interpolation, C.K. Chui et al; and others.