## Approximation with Vector-valued Norms in Linear Spaces |

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### Contents

VECTORNORMS | 6 |

L2 VECTORNORMS | 17 |

GENERALIZED TCHEBYCHEFF EQUIOSCILLATION | 25 |

4 other sections not shown

### Common terms and phrases

alternately positive arcwise connected assumed BACOPOULOS Briefly CHAPTER column player component norms constraints continuity of F continuous function f(x convex sets convexity of F COROLLARY definition degree less denote descending chains electronic filter example exists extremum F(in f(x+ follows formulation of model Fourier coefficients Fourier theory given inner products interpolation k-ball Kuhn and Tucker L3 norm Lagrange multipliers LEMMA linear programming linear space llxll lumped parameters M-norms M(En M(in map under F Matrix Game method minimal set minimum model theory N-NE arc non-linear programming non-negative ordinary norms orthonormal partial extreme points partial order polynomials of degree problem of linear problem of minimizing proof of theorem range of F real-valued function row player seminorms solution to F(a supremum norm Tchebycheff Approximation Tchebycheff theory theorem 3.l thesis tion total extreme uniform norm unique University of Wisconsin usual norm vector vector-norm vector-valued norm x+)(p x+