Peano's kernel theorem for vector-valued functions and some applications. (December 2019)

• Record Type: Journal Article
• Authors: Stefano, De Marchi; Marco, Vianello
• Is Part Of: Numerical functional analysis and optimization. Volume 17:Number 1/2(1996)
• Page Start: 57
• Page End: 64
• Publication Date: 2019-12
• Subjects: Paeno's Kernel Theorem -- vector-valued functions -- Banach spaces -- abstract polynomial interpolation -- abstract quadrature formulas -- abstract parabolic evolution equations -- trapezoidal time discretization method; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630569608816682
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract : We extend the well-known Peano Kernel Theorem to a class of linear operators L : Cn+1([a, b];X}→ X, X being a Branch space, which vanish on abstract polynomials of degree ≤ n. We then recover, in the abstract setting, classical estimates of remainders in polynomials interpolation and quadrature formulas. Finally, we present an application to the error analysis of the trapezoidal time discretization scheme for parabolic evolution equations.