Collected Papers III.M. Gelfand (1913 - 2009), one of the world's leading contemporary mathematicians, largely determined the modern view of functional analysis with its numerous relations to other branches of mathematics, including mathematical physics, algebra, topology, differential geometry and analysis. In this three-volume Collected Papers Gelfand presents a representative sample of his work. Gelfand's research led to the development of remarkable mathematical theories - most of which are now classics - in the field of Banach algebras, infinite-dimensional representations of Lie groups, the inverse Sturm-Liouville problem, cohomology of infinite-dimensional Lie algebras, integral geometry, generalized functions and general hypergeometric functions. The corresponding papers form the major part of the collection. Some articles on numerical methods and cybernetics as well as a few on biology are also included. A substantial number of the papers have been translated into English especially for this edition. The collection is rounded off by an extensive bibliography with almost 500 references. Gelfand's Collected Papers will be a great stimulus, especially for the younger generation, and will provide a strong incentive to researchers. |
Contents
II | 3 |
IV | 18 |
V | 22 |
VI | 31 |
VII | 37 |
VIII | 39 |
X | 41 |
XII | 124 |
LXVII | 556 |
LXIX | 564 |
570 | |
LXXIII | 596 |
LXXIV | 602 |
LXXVI | 605 |
LXXVII | 608 |
LXXIX | 611 |
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Common terms and phrases
a₁ affine space Akad arbitrary C₁ Cartan commutative complex numbers consider constructed corresponding cosets D₁ decomposed decomposition defined denote Diff differential operator dimension direct sum Dokl E₁ eigenvalues elements equal equation equivalent exists finite finite-dimensional formula function g g₁ Gaussian measure Gelfand given group G h₁ h₂ Harish-Chandra Hence Hilbert space homogeneous space horosphere indecomposable integral invariant irreducible representations irreducible unitary representations isomorphism k₁ Lemma Lie algebra linear Lorentz group m₁ manifold mapping Math matrices module monomial multiplication n₁ Nauk SSSR norm obtain P₁ P₂ pair polynomial positive definite proof Proposition prove relation representation of G respect ring satisfying the condition semisimple Lie group sequence space H spherical functions subset subspace symmetric Theorem tion transformation unimodular uniquely unitary representation vector w₁ w₂ Weyl group X₁ z₁ zero