New properties of the Chebyshev polynomials and their applications in variational methods (Q1975793)

The authors use some newly revealed properties of the Chebyshev polynomials of the first kind to derive finite analytical expressions for the scalar products involved in various variational methods, to determine conditions under which a certain scalar product vanish, and to construct approximate solutions to operator equations. The boundary value problem posed for a linear ordinary differential equation is analyzed to demonstrate the possibility of more efficient numerical solution of a broad class of operator equations.