Stability of motion. Applications of Lyapunov's second by N. N. Krasovskii

By N. N. Krasovskii

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A brief introduction to distributions is given in Appendix C. 37) to distributions one must define the convolution of two distributions. To do so one multiplies Eq. 38) on both sides with a smooth test function ϕ ∈ Cc∞ (R ) of compact support. 52) where the notation f (y), ϕ( x + y) means that the functional F f is applied to the function ϕ( x + ·) for fixed x. 2 Mathematical Introduction to Fractional Derivatives where ϕ x (·) = ϕ( x + ·). 52) can be used as a definition for the convolution of distributions provided that the right-hand side has meaning.

2001 – (see [6]) which I found wonderful, by their content and the clarity of the exposition. I regretted strongly that I did not know them before the completion of my latest book. I should greatly appreciate your sending me your latest works in this area. I am attaching a text containing my latest work in this domain. It is a “long version”, not intended for publication as such. It contains many details (it was the basis of some seminars I delivered here). I should sincerely appreciate your having a look at it and letting me know your comments and suggestions.

E. E. Ph. van Milligen, “Renormalization of tracer turbulence leading to fractional differential equations”, Phys. Rev. E 74, 016305 (2006). 2 R. A. Carreras, and B. Ph. van Millegen, “Radu Balescu and the search for a stochastic description of turbulent transport in plasma”, Phys. Ann. Univ. Cracovia 17, 27 (2007) (special issue In Memoriam of Radu C. Balescu (1932–2006)). 3 M. De Leener, J. Orban, M. Pettini, A. H. Misguich, and R. Balescu, in Proceedings of the Congrès Société Francaise de Physique, Nice, 1985, Bull.

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