By Günter Radons, Rainer Klages, Igor M. Sokolov

ISBN-10: 0470046074

ISBN-13: 9780470046074

ISBN-10: 3527403361

ISBN-13: 9783527403363

ISBN-10: 3527404309

ISBN-13: 9783527404308

ISBN-10: 3527406700

ISBN-13: 9783527406708

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Radu Balescu was a master of statistical mechanics with a deep physical insight. He will certainly be missed, but his scientiﬁc legacy will continue to be inﬂuential. 4 My Memory of Radu Balescu by Francesco Mainardi My ﬁrst acquaintance with Radu Balescu was in the late 1990s through his book Statistical Mechanics – Matter out of Equilibrium (Imperial College Press, 1997). I found his treatment of statistical mechanics very innovative compared to those in the classical books and I much appreciated his chapter on nonGaussian stable probability distributions and generalized master equations.

We met a man with the greatest scientiﬁc honesty and as critical with our ideas as he was with his own. Regretfully, this kind of “symmetry” is not commonly found in the competitive arena that scientiﬁc research has become. It is just one of the reasons for which, without a doubt, I can say that he will be missed. 6 Remembering Radu Balescu by Diego del-Castillo-Negrete Radu Balescu once wrote: “I have been ’in love’ with the statistical mechanics of plasma physics over my whole scientiﬁc career” [5].

Then (I1+ f )( x ) → const as x → ∞ and F I1+ f does not exist [94]. 56) can be extended to all α with Re α > 0 for functions in the so-called Lizorkin space [99, p. 148] deﬁned as the space of functions f ∈ S(R ) such that (Dm F { f })(0) = 0 for all m ∈ N0 . 57b) for functions in Lizorkin space. 58) 0 for locally integrable functions f : R + → C. 59) by the convolution theorem for Laplace transforms. The Laplace transform of I0α− f leads to a more complicated operator. 60) a holds. The formula is known as fractional integration by parts [99].

### Anomalous Transport Foundations and Applications by Günter Radons, Rainer Klages, Igor M. Sokolov

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