Stratified Lie Groups and Potential Theory for Their Sub-Laplacians
The existence, for every sub-Laplacian, of a homogeneous fundamental solution smooth out of the origin, plays a crucial role in the book. This makes it possible to develop an exhaustive Potential Theory, almost completely parallel to that of the classical Laplace operator. This book provides an exte...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2007, 2007
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| Edition: | 1st ed. 2007 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Elements of Analysis of Stratified Groups
- Stratified Groups and Sub-Laplacians
- Abstract Lie Groups and Carnot Groups
- Carnot Groups of Step Two
- Examples of Carnot Groups
- The Fundamental Solution for a Sub-Laplacian and Applications
- Elements of Potential Theory for Sub-Laplacians
- Abstract Harmonic Spaces
- The ?-harmonic Space
- ?-subharmonic Functions
- Representation Theorems
- Maximum Principle on Unbounded Domains
- ?-capacity, ?-polar Sets and Applications
- ?-thinness and ?-fine Topology
- d-Hausdorff Measure and ?-capacity
- Further Topics on Carnot Groups
- Some Remarks on Free Lie Algebras
- More on the Campbell–Hausdorff Formula
- Families of Diffeomorphic Sub-Laplacians
- Lifting of Carnot Groups
- Groups of Heisenberg Type
- The Carathéodory–Chow–Rashevsky Theorem
- Taylor Formula on Homogeneous Carnot Groups