Stability Properties of Trigonometric Interpolating Operators,
Abstract
The interpolating operator P studied here is the one which produces a trigonometric polynomial of order n taking prescribed values at 2n + 1 equally-spaced nodes (theta sub j) = 2 pi j (2n + 1), j = 0,...,2n. This operator P acts in the space C of 2 pi-periodic continuous real functions, normed with the supremum norm. For any point, phi, other than a node, there is a (2n + 1)-dimensional manifold of projections carried by the point set ((theta sub o),...,(theta sub 2n), phi). The first theorem states that P is the element of least norm in this manifold. Another theorem asserts that if 3 correctly-chosen points are adjoined to the set of nodes, then P is no longer a minimal element in the manifold of projections carried by that point set. Various other related results are given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1972
- Accession Number
- AD0747540
Entities
People
- E. W. Cheney
- P. D. Morris
Organizations
- University of Texas at Austin