Stratified Lie Groups and Potential Theory for Their Sub-Laplacians / Edition 1

Stratified Lie Groups and Potential Theory for Their Sub-Laplacians / Edition 1

by Andrea Bonfiglioli, Ermanno Lanconelli, Francesco Uguzzoni
     
 

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ISBN-10: 3642090990

ISBN-13: 9783642090998

Pub. Date: 11/10/2010

Publisher: Springer Berlin Heidelberg

This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential

Overview

This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.

Product Details

ISBN-13:
9783642090998
Publisher:
Springer Berlin Heidelberg
Publication date:
11/10/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 2007
Pages:
802
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

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.

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