## Optimal estimation in approximation theory |

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### Contents

A Survey of Optimal Recovery | 2 |

Optimal Estimation of Linear Functionals | 13 |

Examples of Optimal Recovery of Linear Functionals by Linear | 22 |

Copyright | |

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Acta Cryst.A analytic applied approximation theory assume Banach space best approximation Bojanov bound calculation cartographic compact computing constant convex convex set defined denote density function determined differential equations eigenvalues equalization Estimation Problem example exists formula Fourier function f given hence Hilbert space hyperoptimal IFLAG implies inequality information content integral interval Kalman-Bucy filter knots Lemma linear functional linear space Math mathematical matrix method Micchelli minimal error minimal projections n-width nodes noise norm objects obtain ommatidium optimal algorithm optimal filter optimal recovery scheme orthogonal output parameters perfect spline Phase points polynomial Proof properties radiographs rational function reconstruction reproducing kernel result Rivlin satisfying sequence signal solved spline interpolation spline of degree structure subset subspace sup Ux Suppose Theorem tion unique unit ball unit cell values vanishes vector x-ray X-rule zero