On certain Banach spaces in connection with interpolation theory

[摘要] By using a norm generated by the error series of a sequence of interpolation polynomials, we obtain in this paper certain Banach spaces. A relation between these spaces and the space (C-0,S) with norm generated by the error series of the best polynomial approximations (minimax series) is established. Finally, certain inequalities for the minimax series of a product are obtained which permit us to define a product over the space (C-0,S). With such a product (C-0,S) is a Banach Algebra.

[发布日期] 1997-09-30

[关键词] interpolation polynomials;error series;minimax series;convergence;Banach spaces;Banach Algebras