Title
WeierstrassStone,: The Theorem (Approximation and Optimization),Used
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Product Description The WeierstrassStone Theorem is one of the main tools of modern analysis, and several parts of functional analysis would not exist without it. The purpose of this monograph is to present its true nature by proving several increasing generalizations of this theorem, going from the classical case of subalgebras to submodules and to arbitrary subsets of continuous functions over compact spaces. Some closely connected results on uniform approximation which are important for many applications are also presented, namely the ChoquetDeny and the Kakutani Theorems for semilattices and for lattices of continuous functions, respectively. The beautiful variation of the WeierstrassStone Theorem due to von Neumann is also included with the proof due to R. I. Jewett. The monograph ends with several recent results on uniform approximation of bounded continuous functions over noncompact spaces. Review The book is very well written and we recommended it to all people interested in one or several aspects of the WeierstraStone theorem. (C. Badea, Zentralblatt fr Mathematik) About the Author The Author: JoThe Author: Joo B. Prolla was born in 1935. He received his doctorate in 1968 from New York University. Since 1976 he is a full professor at the State University of Campinas, Brazil. His main fields of research are approximation theory and padic functional analysis.
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