Work
Gelfand is known for many developments including:
- the book Calculus of Variations (1963), which he co-authored with Sergei Fomin
- the Gelfand representation in Banach algebra theory;
- the Gelfand–Mazur theorem in Banach algebra theory;
- the Gelfand–Naimark theorem;
- the Gelfand–Naimark–Segal construction;
- Gelfand–Shilov spaces
- the Gelfand–Pettis integral;
- the representation theory of the complex classical Lie groups;
- contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I.N. Bernstein and S.I. Gelfand);
- contributions to distribution theory and measures on infinite-dimensional spaces;
- the first observation of the connection of automorphic forms with representations (with Sergei Fomin);
- conjectures about the Atiyah–Singer index theorem;
- Ordinary differential equations (Gelfand–Levitan theory);
- work on calculus of variations and soliton theory (Gelfand–Dikii equations);
- contributions to the philosophy of cusp forms;
- Gelfand–Fuks cohomology of foliations;
- Gelfand–Kirillov dimension;
- integral geometry;
- combinatorial definition of the Pontryagin class;
- Coxeter functors;
- general hypergeometric functions;
- Gelfand - Tsetlin patterns;
- and many other results, particularly in the representation theory for the classical groups.
Read more about this topic: Israel Gelfand
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