Abstract
1. The subject discussed in this sketch can be characterized in very general terms not connected with any special field of mechanics or physics. For simplicity, we confine ourselves to considering only changes in time of a certain finite number of variables
*
In: Collected papers on the 30th anniversary of the Great October Socialist Revolution, Vol. 1, Akad. Nauk SSSR, Moscow-Leningrad, 1947, pp. 242-252.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Khintchine, ‘Korrelationstheorie der stationären stochastischen Prozesse’, Math. Ann. 109:4 (1934), 604–615.
H. Cramer, ‘On the theory of stationary random processes’, Ann. of Math. 41:1 (1940), 215–230.
E. Slutsky, ‘Sur les fonctions aléatoires presque périodiques et sur la décomposition des fonctions aléatoires stationnaires en composantes’, Actual. Sci. 738 (1938), 35–55.
A.N. Kolmogorov, ‘Interpolation and extrapolation of stationary random sequences’, Izv. Akad. Nauk SSSR Ser. Mat. 5:1 (1941), 3–14 (in Russian) (No. 28 in this volume).
A.N. Kolmogorov, ‘Stationary sequences in Hilbert space’, Byull. Moskov. Gos. Univ. Ser. Mat. 2:6 (1941), 1–40 (in Russian) (No. 27 in this volume).
A.N. Kolmogorov, ‘Curves in Hilbert space invariant with respect to a oneparameter group of motions’, Dokl. Akad. Nauk SSSR 26:1 (1940), 6–9 (in Russian).
A.N. Kolmogorov, ‘Wiener’s spiral and some other interesting curves in Hilbert space’, Dokl. Akad. Nauk SSSR 26 (1940), 115–118 (in Russian).
H. Cramér, ‘On harmonic analysis in certain functional spaces’, Ark. Mat. Astron. Fys. B 28:12 (1942), 1–7.
M. Loève, ‘Analyse harmonique générale d’une fonction aléatoire’, C. R. Acad. Sci. Paris 220:12 (1945), 380–382.
A. Blanc-Lapierre and R. Fortet, ‘Sur la décomposition spectrale de fonction aléatoire stationnaire d’ordre deux’, C. R. Acad. Sci. Paris 222:9 (1946), 467–468.
A. Blanc-Lapierre and R. Fortet, ‘Résultats sur la décomposition spectrale des fonctions aléatoires stationnaires d’ordre 2’, C. R. Acad. Sci. Paris 222:13 (1946), 713–714.
H. Wold, A study in the analysis of stationary time series, Uppsala, 1938; 2nd. ed. 1954.
V.N. Zasukhin, ‘On the theory of multidimensional stationary random processes’, Dokl. Akad. Nauk SSSR 33:5 (1941), 435–437.
E.E. Slutsky, ‘Summation of random causes as a source of cyclic processes’, Voprosy Kon’’yunktury 3:1 (1927), 34–64 (in Russian). English transi: Econometrica 5:2 (1937), 105-146.
E.V. Shpol’skii, Atomic physics, Gostekhizdat, Moscow-Leningrad, 1944 (in Russian).
A.I. Plesner, ‘Spectral theory of linear operators’, Uspekhi Mat. Nauk 9 (1941), 3–124 (in Russian).
A.I. Plesner and V.A. Rokhlin, ‘Spectral theory of linear operators’, Uspekhi Mat. Nauk 1:1 (1946), 192–216 (in Russian).
N. Wiener, The Fourier integral and certain of its applications, New York, 1933.
N. Wiener, ‘The harmonic analysis of irregular motion’, J. Math. Phys. 5 (1926), 99–122, 158-191.
A.N. Kolmogorov, Basic notions of probability theory, ONTI, Moscow-Leningrad, 1936; 2nd ed. Nauka, Moscow, 1974 (in Russian).
Editor information
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Shiryayev, A.N. (1992). Statistical Theory of Oscillations with Continuous Spectrum. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_34
Download citation
DOI: https://doi.org/10.1007/978-94-011-2260-3_34
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5003-6
Online ISBN: 978-94-011-2260-3
eBook Packages: Springer Book Archive