Collected Papers I

I.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.

I. Survey lectures and articles of general content.- 1. Some aspects of functional analysis and algebra.- 2. On some problems of functional analysis.- 3. Some questions of analysis and differential equations.- 4. Integral geometry and its relation to the theory of group representations.- 5. On elliptic equations.- 6. Automorphic functions and the theory of representations.- 7. The cohomology of infinite dimensional Lie algebras; some questions of integral geometry.- II. Banach spaces and normed rings.- 1. Sur un lemme de la theorie des espaces lineaires.- 2. Abstrakte Funktionen und lineare Operatoren.- 3. On one-parametrical groups of operators in a normed space.- 4. On normed rings.- 5. To the theory of normed rings. II. On absolutely convergent trigonometrical series and integrals.- 6. To the theory of normed rings. III. On the ring of almost periodic functions.- 7. On the theory of characters of commutative topological groups.- 8. Normierte Ringe.- 9. Über verschiedene Methoden der Einführung der Topologie in die Menge der maximalen Ideale eines normierten Ringes.- 10. Ideale und primare Ideale in normierten Ringen.- 11. Zur Theorie der Charaktere der Abelschen topologischen Gruppen.- 12. Über absolut konvergente trigonometrische Reihen und Integrale.- 13. On the imbedding of normed rings into the ring of operators in Hilbert space.- 14. Commutative normed rings.- 15. Normed rings with an involution and their representations.- III. Differential equations and mathematicalphysics.- 1. Eigenfunction expansions for equations with periodic coefficients.- 2. On the determination of a differential equation from its spectral function.- 3. On a simple identity for eigenvalues of second order differential operator.- 4. Solution of quantum field equations.- 5. On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients.- 6. Eigenfunction expansions for differential and other operators.- 7. On identities for eigenvalues of a second order differential operator.- 8. Some problems in the theory of quasilinear equations.- 9. On a theorem of Poincare.- 10. Fractional powers of operators and Hamiltonian systems.- 11. A family of Hamiltonian structures related to nonlinear integrable differential equations.- 12. Asymptotic behaviour of the resolvent of Sturm-Liouville equations and the algebra of the Korteweg-de Vries equations.- 13. The resolvent and Hamiltonian systems.- 14. Integrable nonlinear equations and the Liouville theorem.- 15. Hamiltonian operators and algebraic structures related to them.- 16. The Schouten bracket and Hamiltonian operators.- 17. Hamiltonian operators and the classical Yang-Baxter equation.- Essays in honour of Izrail M. Gelfand.- On his fiftieth birthday.- On his sixtieth birthday.- On his seventieth birthday.- Some remarks on I.M. Gelfand's works.- Some remarks on I.M. Gelfand's works.- Tentative table of contents for volumes II and III.- Acknowledgements.