Selected Works I

1. A Fourier-Lebesgue series divergent almost everywhere.- 2. On the order of magnitude of the coefficients of Fourier-Lebesgue series.- 3. A remark on the study of the convergence of Fourier series.- 4. On convergence of Fourier series (in collaboration with G.A. Seliverstov).- 5. Axiomatic definition of the integral.- 6. On the limits of generalization of the integral.- 7. On the possibility of a general definition of derivative, integral and summation of divergent series.- 8. On conjugate harmonic functions and Fourier series.- 9. On the tertium non datur principle.- 10. On convergence of Fourier series (in collaboration with G.A. Seliverstov).- 11. A Fourier-Lebesgue series divergent of everywhere.- 12. On convergence of series of orthogonal functions (in collaboration with D.E. Men’shov).- 13. On operations on sets.- 14. On the Denjoy integration process.- 15. On the topological group-theoretic foundation of geometry.- 16. Studies on the concept of integral.- 17. On the notion ofmean.- 18. On the compactness of sets of functions in the case of convergence in mean.- 19. On the interpretation of intuitionistic logic.- 20. On the foundation of projective geometry.- 21. On measure theory.- 22. On points of discontinuity offundions of two variables (in collaboration with LYa. Verchenko).- 23. On normability of a general topological linear space.- 24. Continuation of the study of points of discontinuity of functions of two variables (in collaboration with LYa. Verchenko).- 25. On the convergence of series in orthogonal polynomials.- 26. Laplace transformation in linear spaces.- 27. On the order of magnitude of the remainder term in the Fourier series of differentiable functions.- 28. On the best approximation of functions of a given class.- 29. On duality in combinatorial topology.- 30. Homology rings of complexes and locally bicompact spaces.- 31. Finite coverings of topological spaces (in collaboration with P.S. Aleksandrov).- 32. The Betti groups of locally bicompact spaces.- 33. Properties of the Betti groups of locally bicompact spaces.- 34. The Betti groups of metric spaces.- 35. Relative cycles. The Alexander duality theorem.- 36. On open mappings.- 37. Skew-symmetric forms and topological invariants.- 38. A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem (in collaboration with I.G. Petrovskii and N.S. Piskunov).- 39. A simplified proof of the Birkhoff-Khinchin ergodic theorem.- 40. On inequalities for suprema of consecutive derivatives of an arbitrary function on an infinite interval.- 41. On rings of continuous functions on topological spaces (in collaboration with I.M. Gel’fand).- 42. Curves in a Hilbert space invariant with respect to a one-parameter group of motions.- 43. Wiener spirals and some other interesting curves in a Hilbert space.- 44. Points of local topological character of count ably-multiple open mappings of compacta.- 45. Local structure of turbulencein an incompressible viscous fluid at very large Reynolds numbers.- 46. On the degeneration of isotropic turbulence in an incompressible viscous fluid.- 47. Dissipation of energy in isotropic turbulence.- 48. Equations of turbulent motion in an incompressible fluid.- 49. A remark on Chebyshev polynomials least deviating from a given function.- 50. On the breakage of drops in a turbulent flow.- 51. On dynamical systems with an integral invariant on a torus.- 52. On the preservation of conditionally periodic motions under small variations of the Hamilton function.- 53. The general theory of dynamical systems and classical mechanics.- 54. Some fundamental problems in the approximate and exact representation of functions of one or several variables.- 55. On the representation of continuous functions of several variables as superpositions of continuous functions of a smaller number of variables.- 56. On the representation of continuous functions of several variables as superpositions of continuous functions of one variable and addition.- 57. On the linear dimension of topological vector spaces.- 58. A refinement of the concept of the local structure of turbulence in an incompressible viscous fluid at large Reynolds numbers.- 59. P.S. Aleksandrov and the theory of 8s-operations.- 60. A qualitative study of mathematical models of population dynamics.- Commentary.- List of works by A.N. Kolmogorov.