Collected Papers I

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 mathematical physics.- 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.