Abstract
Improving a recent result by the authors, a vector-valued version of Peano's Kernel Theorem is proposed, which gives an integral estimate for a class of linear operators , with X general normed space, vanishing on all abstract polynomials of degree < n. Continuity and derivatives are intended in the weak sense. When lthe space is complete, the usual integral representation is retrieved. We show that all usual remainder estimates for polynomial, piecewise polynomial, and spline polynomial interpolation, numerical differentiation and numerical quadrature, can be readily transferred in the vector-valued setting.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
