Construction of a Gibbs measure associated to the periodic Benjamin–Ono equation

We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin–Ono eq...

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Veröffentlicht in:	Probability theory and related fields 2010-03, Vol.146 (3-4), p.481-514, Article 481
1. Verfasser:	Tzvetkov, N.
Format:	Artikel
Sprache:	eng
Schlagworte:	Construction Economics Exact sciences and technology Finance General topics Hilbert space Insurance Management Mathematical analysis Mathematical and Computational Biology Mathematical and Computational Physics Mathematical functions Mathematics Mathematics and Statistics Operations Research/Decision Theory Ordinary differential equations Probability Probability and statistics Probability Theory and Stochastic Processes Quantitative Finance Sciences and techniques of general use Sobolev space Statistics for Business Studies Theoretical
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Zusammenfassung:	We define a finite Borel measure of Gibbs type, supported by the Sobolev spaces of negative indexes on the circle. The measure can be seen as a limit of finite dimensional measures. These finite dimensional measures are invariant by the ODE’s which correspond to the projection of the Benjamin–Ono equation, posed on the circle, on the first N , N ≥ 1 modes in the trigonometric bases.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s00440-008-0197-z