Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one.

This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory.

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"The book is written in a very concise, clear, and elegant way. Misprints are rare... There are no exercises, but the book is well equipped with examples, which help to understand the assertions and are, as a rule, of independent interest. To sum up, the text presents an extremely interesting account of some of the most important developments in the chosen direction."

―MATHEMATICAL REVIEWS

"The boal of the book under review is to present a method for examing the surprising connection between invariant differential operators and almost periodic operators on Lie groups with polynomial growth. . . The book is deveoted to a very interesting topic. It is aimed to graduate studetns as well as researchers, and it can be highly recommended."

---ZAA

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