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On the Canonical Form of Turbulence

Published online by Cambridge University Press:  22 January 2016

Seizô Itô
Seizô Itô*
Affiliation:
Mathematical Institute, Nagoya University
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In K, Itô’s paper [1] on the theory of turbulence, the problem to determine the canonical form of the moment tensor of temporally homogeneous and isotropic turbulence, has not been solved. In the present paper, the author will solve the problem by making use of the result of his preceding paper [2]. We shall treat the turbulence in R3 but the similar argument is possible in Rn.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 2 , February 1951 , pp. 83 - 92
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1951

References

Literature

[1] Itô, K.: A kinematic theory of turbulence, Proc. Imp. Acad. Tokyo, 20, No. 3 (1944), pp. 120–122.Google Scholar
[2] Itô, S.: Positive definite functions on homogeneous spaces, Proc. Japan Acad. 26, No. 1 (1950), pp. 17-28.Google Scholar
[3] Haviland, E. K.: On the inversion formula for Fourier-Stieltjes transforms in more one dimension, Amer. Journ. Math. 57(1935), pp. 94-100 & 382-388.Google Scholar
[4] Ambrose, W.: Spectral resolution of groups of unitary operators, Duke Math. Journ. 11, No. 3 (1944).Google Scholar
[5] Weil, A.: L’integration dans les groupes topologiques et ses applications, Act. Sci. Ind. Paris, 869 (1940).Google Scholar
[6] Saks, S.: Theory of the integral, Warsaw (1937).Google Scholar