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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Interpolation to analytic data on unbounded curves


Author: Maynard Thompson
Journal: Trans. Amer. Math. Soc. 167 (1972), 309-318
MSC: Primary 30A80
MathSciNet review: 0298027
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Abstract: This paper provides a method for constructing a family of sets of points on the boundary (assumed suitably smooth) of an unbounded Jordan region in the complex plane which is useful for certain interpolation problems. It is proved that if these sets are used as nodes for Lagrange interpolation to analytic data, then the resulting polynomials converge in the region, and the limit function is related in a natural way to the boundary data. Subsidiary results include an approximate quadrature formula for slowly decreasing functions on an infinite interval.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0298027-3
PII: S 0002-9947(1972)0298027-3
Keywords: Polynomial interpolation on unbounded regions, rational approximation, approximate quadrature
Article copyright: © Copyright 1972 American Mathematical Society