Interpolation to analytic data on unbounded curves

Thompson, Maynard

doi:10.1090/S0002-9947-1972-0298027-3

Interpolation to analytic data on unbounded curves
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Trans. Amer. Math. Soc. 167 (1972), 309-318 Request permission

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.

References

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19

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