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The book is devoted to the mathematical foundations of nonextensive
statistical mechanics. This is the first book containing the
systematic presentation of the mathematical theory and concepts
related to nonextensive statistical mechanics, a current
generalization of Boltzmann-Gibbs statistical mechanics introduced
in 1988 by one of the authors and based on a nonadditive entropic
functional extending the usual Boltzmann-Gibbs-von Neumann-Shannon
entropy. Main mathematical tools like the q-exponential function,
q-Gaussian distribution, q-Fourier transform, q-central limit
theorems, and other related objects are discussed rigorously with
detailed mathematical rational. The book also contains recent
results obtained in this direction and challenging open problems.
Each chapter is accompanied with additional useful notes including
the history of development and related bibliographies for further
reading.
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