## Collected Papers, Volume 1I.M. Gelfand, one of the 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. With the publication of these Collected Papers in three volumes Gelfand gives a representative choice of his papers written in the last fifty years. Gelfand's research led to the development of remarkable mathematical theories - most 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 Collected Papers. Some articles on numerical methods and cybernetics as well as a few on biology are included. A substantial part of the papers have been translated into English especially for this edition. This edition 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 give an incentive to researchers. |

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### Contents

Some aspects of functional analysis and algebra | 3 |

On some problems of functional analysis | 29 |

Some questions of analysis and differential equations | 37 |

Copyright | |

38 other sections not shown

### Common terms and phrases

Akad Anal arbitrary asymptotic Bedingung beliebiges boundary conditions cells coefficients cohomology commutative compact complex numbers consider constructed continuous function convergent corresponding curve defined definition denote derivatives determined differential equations differential operator discontinuity Dokl eigenvalues element example exists finite Folge Folglich folgt follows formula Funktionen Funkts group G group ring Hamiltonian Hence Hilbert space homogeneous space homomorphism I. M. Gel'fand infinite-dimensional integral geometry invariant inverse inverse element irreducible representations isomorphic kompakt Konvergenz Korteweg-de Vries equation Lemma Lie algebra Lie groups linear M.I. Graev manifold mapping Math matrix maximal ideals Menge multipliers Nauk SSSR normed ring obtain Poisson brackets polynomials Prilozh problem proof proved Raum Russian satisfying the conditions Satz schwach solution spectral stetig subgroup symplectic Theorem theory tion topological unitary representations values variables Variation Vasil'ev vector fields Yu.M zero