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

Karlin, Samuel

doi:10.1090/S0002-9947-1975-0367512-0

Interpolation properties of generalized perfect splines and the solutions of certain extremal problems. I
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Trans. Amer. Math. Soc. 206 (1975), 25-66 Request permission

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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