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Functional Analysis and Semi-Groups

By Hille, Einar

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Book Id: WPLBN0000673944
Format Type: PDF eBook
File Size: 816.05 KB
Reproduction Date: 2005
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Title: Functional Analysis and Semi-Groups  
Author: Hille, Einar
Language: English
Subject: Science., Mathematics, Logic
Publication Date:


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Hille, E. (n.d.). Functional Analysis and Semi-Groups. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: Seven years have now elapsed since the publication of the first edition of this treatise in October 1948. The friendly interest which the mathematical community has shown for this work has been most gratifying; in fact, the edition was out of print by 1954. We can also report the appearance of a Russian translation of the book in 1951 [Funkcional'nyj Analiz i Polugruppy, Izdatel'stvo Innostrannoj Literatury, Moskva, 1951,636 pages]. Since 1948 both the analytical theory of semi-groups and its applications have made vigorous progress. K. Yosida found the basic generation theorem independently of Hille in 1948 and proceeded to apply it to the diffusion equation in a series of important papers. Inspired by Yosida's work, Hille made a new attack on Cauchy's problem with the aid of semi-group theory, starting in 1949. Soon thereafter, W. Feller became interested in the possibilities of the new approach and he and his students have contributed much to the theory; we mention in particular his penetrating investigation of the singular boundary value problem for the diffusion equation. Another of the early workers in the general theory of semi-groups of linear operators was R. S. Phillips who filled in many of the gaps which Hille had left behind and then went on to broaden the theory using representation theory for semi-group algebras, perturbation methods, extended classes of semi-groups, and adjoint semi-groups. In a different direction, in 1948 Hille laid the foundations of a Lie theory of semi-groups.


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