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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Interpolation properties of generalized perfect splines and the solutions of certain extremal problems. I


Author: Samuel Karlin
Journal: Trans. Amer. Math. Soc. 206 (1975), 25-66
MSC: Primary 41A15
DOI: https://doi.org/10.1090/S0002-9947-1975-0367512-0
MathSciNet review: 0367512
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Abstract: The existence of generalized perfect splines satisfying certain interpolation and/or moment conditions are established. In particular, the existence of ordinary perfect splines obeying boundary and interpolation conditions is demonstrated; precise criteria for the uniqueness of such interpolatory perfect splines are indicated. These are shown to solve a host of variational problems in certain Sobolev spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0367512-0
Article copyright: © Copyright 1975 American Mathematical Society