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Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

Paperback

Series: Springer Monographs in Mathematics

General Mathematics

ISBN10: 3642090990
ISBN13: 9783642090998
Publisher: Springer
Published: Nov 11 2010
Pages: 802
Weight: 2.51
Height: 1.65 Width: 6.14 Depth: 9.21
Language: English
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.

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Bonfiglioli, Andrea

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General Mathematics