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.

Read more about this topic:  Israel Gelfand

Famous quotes containing the word work:

    “And men left down their work and came,
    And women with petticoats coloured like flame.
    And little bare feet that were blue with cold,
    Went dancing back to the age of gold,
    And all the world went gay, went gay,
    For half an hour in the street to-day.”
    —“Seumas” “O’Sullivan” (1879–1958)

    “So is the English Parliament provincial. Mere country bumpkins, they betray themselves, when any more important question arises for them to settle, the Irish question, for instance,—the English question why did I not say? Their natures are subdued to what they work in. Their “good breeding” respects only secondary objects.”
    —Henry David Thoreau (1817–1862)

    “‘Tis not need we know our every thought
    Or see the work shop where each mask is wrought
    Wherefrom we view the world of box and pit,
    Careless of wear, just so the mask shall fit
    And serve our jape’s turn for a night or two.”
    —Ezra Pound (1885–1972)