A Haar-type theory of best -approximation with constraints

Authors:
András Kroó and Darrell Schmidt

Journal:
Trans. Amer. Math. Soc. **331** (1992), 301-319

MSC:
Primary 41A29; Secondary 41A52

DOI:
https://doi.org/10.1090/S0002-9947-1992-1062190-X

MathSciNet review:
1062190

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Abstract | References | Similar Articles | Additional Information

Abstract: A general setting for constrained -approximation is presented. Let be a finite dimensional subspace of and be a linear operator from to where is a finite union of disjoint, closed, bounded intervals. For with , the approximating set is and the norm is where a positive continuous function on . We obtain necessary and sufficient conditions for to admit unique best -approximations to all for all positive continuous and all satisfying a nonempty interior condition. These results are applied to several -approximation problems including polynomial and spline approximation with restricted derivatives, lacunary polynomial approximation with restricted derivatives, and others.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1062190-X

Keywords:
-approximation with constraints,
-spaces,
-spaces

Article copyright:
© Copyright 1992
American Mathematical Society