Selected Works I: Mathematics and Mechanics 1st ed. 1991 [Pehme köide]

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. Menshov).-
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. Gelfand).-
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.