Kergin interpolation in Banach spaces
2004 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 127, no 1, 108-123 p.Article in journal (Refereed) Published
We show that Kergin interpolation, a generalized Lagrange-Hermite polynomial interpolation, may be defined on mappings between general Banach spaces. Like its finite-dimensional counterpart, Kergin interpolation in this setting is an affine-invariant projector. We obtain an error formula which we use to approximate holomorphic mappings. As an application we give a convergence theorem applicable to, for instance, operators on Banach algebras, such as the algebra of square matrices with complex coefficients.
Place, publisher, year, edition, pages
2004. Vol. 127, no 1, 108-123 p.
Banach space, Kergin interpolation, Lagrange interpolation, operator polynomial
IdentifiersURN: urn:nbn:se:kth:diva-23386DOI: 10.1016/j.jat.2004.01.002ISI: 000221247300006ScopusID: 2-s2.0-2442697529OAI: oai:DiVA.org:kth-23386DiVA: diva2:342084
QC 20100525 QC 201110312010-08-102010-08-102011-10-31Bibliographically approved