Israel Gelfand - Work

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.

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    “You live on hopes, I guess. You always dream that someday you might have a lot of money, your ship might come in. But if the ship doesn’t come in, I’m going to work as long as I can.”
    —Marion Gray (b. c. 1914)

    “I see no reason for calling my work poetry except that there is no other category in which to put it.”
    —Marianne Moore (1887–1972)

    “The true poem is not that which the public read. There is always a poem not printed on paper,... in the poet’s life. It is what he has become through his work. Not how is the idea expressed in stone, or on canvas or paper, is the question, but how far it has obtained form and expression in the life of the artist. His true work will not stand in any prince’s gallery.”
    —Henry David Thoreau (1817–1862)