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

2007
ISBN: 978-3-540-71897-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 802 Seiten, eBook

Reihe: Springer Monographs in Mathematics

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.

1) ERMANNO LANCONELLI: --Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics). Career/Employment: 1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the 'Accademia dell'Istituto di Bologna' and of the 'Accademia delle Scienze, Lettere ed Arti di Modena'. 1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna. --Academic activity: Director of the Istituto di Matematica di Bologna(1978/80), Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present) Director of PHD program, University of Bologna (1986/91, 1997/2000) --INVITATIONS: -University of Minnesota, Minneapolis (USA) -University of Purdue, West La Fayette, Indiana (USA) -Temple University, Philadelphia, Pennsylvania (USA) -Rutgers University, New Brunswick, New Jersey (USA) -University of Bern, Switzerland -- Specialization main fields: Partial Differential Equations, Potential Theory --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes. Potential Theory and Harmonic Analysis in sub-riemannian settings. Real analysis and geometric methods. --EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser. --PUBLICATIONS: More than 70 papers in refereed journals. 2) UGUZZONI FRANCESCO: --Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics) Career/Employment: February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings. --PUBLICATIONS: About 30 papers in refereed journals. 3) ANDREA BONFIGLIOLI: --Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics) --Career/Employment: March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups. --PUBLICATIONS: About 20 papers in refereed journals.

Zielgruppe

Research

Autoren/Hrsg.

Bonfiglioli, Andrea

Lanconelli, Ermanno

Uguzzoni, Francesco

Inhaltsverzeichnis

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.

Über Autor(innen)

1) ERMANNO LANCONELLI:--Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics).Career/Employment:1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the "Accademia dell'Istituto di Bologna" and of the "Accademia delle Scienze, Lettere ed Arti di Modena".1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna.--Academic activity: Director of the Istituto di Matematica di Bologna(1978/80),Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present)Director of PHD program, University of Bologna (1986/91, 1997/2000)--INVITATIONS:-University of Minnesota, Minneapolis (USA)-University of Purdue, West La Fayette, Indiana (USA)-Temple University, Philadelphia, Pennsylvania (USA)-Rutgers University, New Brunswick, New Jersey (USA)-University of Bern, Switzerland-- Specialization main fields: Partial Differential Equations, PotentialTheory--CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes.Potential Theory and Harmonic Analysis in sub-riemannian settings.Real analysis and geometric methods.--EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser.--PUBLICATIONS: More than 70 papers in refereed journals.2) UGUZZONI FRANCESCO:--Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics)Career/Employment:February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy).October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna.--CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings.--PUBLICATIONS: About 30 papers in refereed journals.3) ANDREA BONFIGLIOLI:--Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics)--Career/Employment:March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy).November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna.--CURRENT RESEARCH INTEREST: Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups.--PUBLICATIONS: About 20 papers in refereed journals.