Introduction to Approximation Theory (AMS Chelsea Publishing) - ISBN:0821813749

Introduction to Approximation Theory (AMS Chelsea Publishing)

Date: 13 April 2011, 00:37

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In writing this book I have sought to bring a large segment of approximation theory within the comfortable grasp of undergraduate and beginning graduate mathematics students. This goal would not be a reasonable one were it not for the fact that traditionally much of the activity in this discipline has been directed toward uniform approximation on the real line, and that many of the most appealing results in the theory are based upon elementary real-variable arguments. Nevertheless, this pedagogical framework dictates a certain bias in the choice of topics. In particular, approximation with integral norms has been deemphasized in favor of uniform (or "TchebychefP,) approximation. This has made it unnecessary to presuppose the Lebesgue integral or measure theory. Further, in order not to require of the reader a knowledge of complex function theory, the discussion has been directed to problems involving only real-valued functions of real variables. We do not presuppose any "modern" algebra except elementary linear space theory.

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