Bonfiglioli / Lanconelli / Uguzzoni Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

1. Auflage 2007
ISBN: 978-3-540-71897-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 802 Seiten

Autoren/Hrsg.

Bonfiglioli, Andrea

Lanconelli, Ermanno

Uguzzoni, Francesco

Inhaltsverzeichnis

1;Preface;6
2;Contents;19
3;Elements of Analysis of Stratified Groups;25
3.1;1 Stratified Groups and Sub-Laplacians;26
3.2;2 Abstract Lie Groups and Carnot Groups;109
3.3;3 Carnot Groups of Step Two;177
3.4;4 Examples of Carnot Groups;204
3.5;5 The Fundamental Solution for a Sub-Laplacian and Applications;248
4;Elements of Potential Theory for Sub- Laplacians;355
4.1;6 Abstract Harmonic Spaces;356
4.2;7 The L- harmonic Space;400
4.3;8 L- subharmonic Functions;415
4.4;9 Representation Theorems;443
4.5;10 Maximum Principle on Unbounded Domains;491
4.6;11 L- capacity, L- polar Sets and Applications;507
4.7;12 L- thinness and L- fine Topology;555
4.8;13 d- Hausdorff Measure and L- capacity;574
5;Further Topics on Carnot Groups;592
5.1;14 Some Remarks on Free Lie Algebras;593
5.2;15 More on the Campbell–Hausdorff Formula;608
5.3;16 Families of Diffeomorphic Sub-Laplacians;635
5.4;17 Lifting of Carnot Groups;662
5.5;18 Groups of Heisenberg Type;694
5.6;19 The Carathéodory–Chow–Rashevsky Theorem;728
5.7;20 Taylor Formula on Homogeneous Carnot Groups;745
6;References;784
7;Index of the Basic Notation;799
8;Index;805