We extend the well-known Peano Kernel Theorem to a class of linear operators L : C^{n+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.
Peano's kernel theorem for vector-valued functions and some applications
DE MARCHI, STEFANO;VIANELLO, MARCO
1996
Abstract
We extend the well-known Peano Kernel Theorem to a class of linear operators L : C^{n+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.
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