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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Weierstrass-Stone,: The Theorem

Weierstrass-Stone,: The Theorem

Prolla, Joao B.
Brosowski, Bruno

Paperback

Series: Approximation and Optimization, Book 5

Calculus

Currently unavailable to order

ISBN10: 3631465114
ISBN13: 9783631465110
Publisher: Peter Lang
Published: Nov 1 1993
Pages: 130
Language: English
The Weierstrass-Stone 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 Choquet-Deny and the Kakutani Theorems for semi-lattices and for lattices of continuous functions, respectively. The beautiful variation of the Weierstrass-Stone 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 non-compact spaces.

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