"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. The text is self-contained, including a review of
well established local theory for elliptic operators, a summary of the
essential aspects of Lie group theory, numerous illustrative examples,
and open questions. The work is aimed at the graduate students as well
as researchers in the above areas.
Reviews / Votes
"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
Series
Edition
Language
Place of publication
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 23 mm
Weight
ISBN-13
978-0-8176-3225-0 (9780817632250)
DOI
10.1007/978-1-4612-2062-6
Schweitzer Classification
I Introduction.- II General Formalism.- II.1 Lie groups and Lie algebras.- II.2 Subelliptic operators.- II.3 Subelliptic kernels.- II.4 Growth properties.- II.5 Real operators.- II.6 Local bounds on kernels.- II.7 Compact groups.- II.8 Transference method.- II.9 Nilpotent groups.- II.10 De Giorgi estimates.- II.11 Almost periodic functions.- II.12 Interpolation.- Notes and Remarks.- III Structure Theory.- III.1 Complementary subspaces.- III.2 The nilshadow; algebraic structure.- III.3 Uniqueness of the nilshadow.- III.4 Near-nilpotent ideals.- III.5 Stratified nilshadow.- III.6 Twisted products.- III.7 The nilshadow; analytic structure.- Notes and Remarks.- IV Homogenization and Kernel Bounds.- IV.1 Subelliptic operators.- IV.2 Scaling.- IV.3 Homogenization; correctors.- IV.4 Homogenized operators.- IV.5 Homogenization; convergence.- IV.6 Kernel bounds; stratified nilshadow.- IV.7 Kernel bounds; general case.- Notes and Remarks.- V Global Derivatives.- V.1 L2-bounds.- V.2 Gaussian bounds.- V.3 Anomalous behaviour.- Notes and Remarks.- VI Asymptotics.- VI. 1 Asymptotics of semigroups.- VI.2 Asymptotics of derivatives.- Notes and Remarks.- Appendices.- A.1 De Giorgi estimates.- A.2 Morrey and Campanato spaces.- A.3 Proof of Theorem II.10.5.- A.4 Rellich lemma.- Notes and Remarks.- References.- Index of Notation.
