Limits of interpolatory processes
Author:
W. R. Madych
Journal:
Trans. Amer. Math. Soc. 355 (2003), 11091133
MSC (2000):
Primary 41A05, 41A15
Published electronically:
October 25, 2002
MathSciNet review:
1938748
Fulltext PDF Free Access
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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 wellbehaved 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, U9, University of Connecticut, Storrs, Connecticut 062693009
Email:
madych@uconn.edu
DOI:
http://dx.doi.org/10.1090/S0002994702031768
PII:
S 00029947(02)031768
Received by editor(s):
April 11, 2002
Published electronically:
October 25, 2002
Article copyright:
© Copyright 2002 American Mathematical Society
