Abstract
THIS work of Prof. Einar Hille is one of the important mathematical books of the century ; it should be read seriously by every mathematician. The subject of semi-groups is one of great and growing importance, and the type of analysis on which its treatment is based—abstract spaces, linear operations, vector-valued functions, and general analysis in 'Banach algebras'—is scarcely less important. Functional Analysis and Semi-Groups By Prof. Einar Hille. (American Mathematical Society: Colloquium Publications, Vol. 31.) Pp. xi + 528. New York: American Mathematical Society, 1948.) 7.50 dollars.
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