Israel Moiseevich Gel'fand Guide, Meaning , Facts, Information and Description

Israel Moiseevich Gel'fand (born 1913 in Okny, Kherson, then in Russia) is a prolific mathematician in the field of functional analysis, which he interprets in a broad sense as the mathematics of quantum mechanics. He has collaborated on papers with many others — for many years in Moscow, where he ran a seminar before he took a position at Rutgers University. He also for a long time took an interest in cell biology.

He is known for many developments including:

• the Gelfand representation in Banach algebra theory;
• the Gel'fand-Naimark theorem;
• the Gelfand-Naimark-Segal construction
• the representation theory of the complex classical Lie groups;
• contributions to distribution theory and measures on infinite-dimensional spaces;
• the first observation of the connection of automorphic forms with representations (with Fomin);
• conjectures about the index theorem;
• ODEs (Gel'fand-Levitan theory);
• work on calculus of variations and soliton theory (Gel'fand-Dikii equations);
• contributions to the philosophy of cusp forms;
• Gel'fand-Fuks cohomology of foliations;
• Gel'fand-Kirillov dimension;
• integral geometry;
• combinatorial definition of the Pontryagin class;
• Coxeter functors;
• generalised hypergeometric series;

and many other results, particularly in the representation theory for the classical groups.

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