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Global Analysis in Mathematical Physics - Geometric and Stochastic Methods (Hardcover, 1997 ed.)
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Global Analysis in Mathematical Physics - Geometric and Stochastic Methods (Hardcover, 1997 ed.)
Series: Applied Mathematical Sciences, 122
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The first edition of this book entitled Analysis on Riemannian
Manifolds and Some Problems of Mathematical Physics was published
by Voronezh Univer sity Press in 1989. For its English edition, the
book has been substantially revised and expanded. In particular,
new material has been added to Sections 19 and 20. I am grateful to
Viktor L. Ginzburg for his hard work on the transla tion and for
writing Appendix F, and to Tomasz Zastawniak for his numerous
suggestions. My special thanks go to the referee for his valuable
remarks on the theory of stochastic processes. Finally, I would
like to acknowledge the support of the AMS fSU Aid Fund and the
International Science Foundation (Grant NZBOOO), which made
possible my work on some of the new results included in the English
edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995
Preface to the Russian Edition The present book is apparently the
first in monographic literature in which a common treatment is
given to three areas of global analysis previously consid ered
quite distant from each other, namely, differential geometry and
classical mechanics, stochastic differential geometry and
statistical and quantum me chanics, and infinite-dimensional
differential geometry of groups of diffeomor phisms and
hydrodynamics. The unification of these topics under the cover of
one book appears, however, quite natural, since the exposition is
based on a geometrically invariant form of the Newton equation and
its analogs taken as a fundamental law of motion."
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