Analysis on Lie Groups with Polynomial Growth: 214 - Brossura

Dungey, Nick; Ter Elst, A.F.M. (Tom); Robinson, Derek William

Brossura

ISBN 10: 1461273994 ISBN 13: 9781461273998

Casa editrice: Birkhäuser, 2011

Riassunto

"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.

Su questo libro

Recensione

"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

Contenuti

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.1.1 Compact derivatives.- V.1.2 Nilpotent derivatives.- 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.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1461273994
• ISBN 13: 9781461273998
• Rilegatura: Copertina flessibile
• Numero di pagine: 324
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania