Limits of interpolatory processes

Author:
W. R. Madych

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1109-1133

MSC (2000):
Primary 41A05, 41A15

Published electronically:
October 25, 2002

MathSciNet review:
1938748

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Abstract | References | Similar Articles | Additional Information

Abstract: Given distinct real numbers and a positive approximation of the identity , which converges weakly to the Dirac delta measure as goes to zero, we investigate the polynomials which solve the interpolation problem

with prescribed data . More specifically, we are interested in the behavior of when the data is of the form for some prescribed function . One of our results asserts that if is sufficiently nice and has sufficiently well-behaved moments, then converges to a limit which can be completely characterized. As an application we identify the limits of certain fundamental interpolatory splines whose knot set is , where is an arbitrary finite subset of the integer lattice , as their degree goes to infinity.

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Additional Information

**W. R. Madych**

Affiliation:
Department of Mathematics, U-9, University of Connecticut, Storrs, Connecticut 06269-3009

Email:
madych@uconn.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-02-03176-8

Received by editor(s):
April 11, 2002

Published electronically:
October 25, 2002

Article copyright:
© Copyright 2002
American Mathematical Society