Direct and Projective Limits of Geometric Banach Structures.
1st Edition
Published on 6. October 2023
Book
Hardback
472 pages
978-1-032-56171-4 (ISBN)
Description
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced.
Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics.
This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics.
This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
More details
Series
Language
English
Place of publication
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional and scholarly
Postgraduate and Professional
Illustrations
4 s/w Abbildungen, 4 s/w Photographien bzw. Rasterbilder
4 Halftones, black and white; 4 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 31 mm
Weight
898 gr
ISBN-13
978-1-032-56171-4 (9781032561714)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Patrick Cabau | Fernand Pelletier
Direct and Projective Limits of Geometric Banach Structures.
E-Book
10/2023
1st Edition
Chapman & Hall/CRC
€73.99
Available for download
Patrick Cabau | Fernand Pelletier
Direct and Projective Limits of Geometric Banach Structures.
E-Book
10/2023
1st Edition
Chapman & Hall/CRC
€73.99
Available for download
Persons
Patrick Cabau is an independent researcher. He received his M.Sc. at the University of Toulouse in 1980, l'Agregation de Mathematiques in 1987 and his Ph.D. from the University of Savoy in 1999. He has taught at the ENSET (University Nord-Madagascar), has been a member of the LIM (Tunisia Polytechnic School) and a teacher in high schools. His primary current interests are in the areas of differential geometry, mechanics and mathematical physics.
Fernand Pelletier began his career as a researcher at the University of Burgundy in 1970. He obtained his third cycle doctorate in 1973 and his habilitation in 1980 at this University. Appointed Professor at the University of Corsica Pasquale Paoli in 1983, he was transferred to the University of Savoy in 1986. He was the Director of the Mathematics Laboratory (LAMA) of the University of Savoy from 1989 to 1996, Director of differential geometry teams in LAMA from 1996 to 2002 and Director of the "South Rodhanian" research group from 2002 to 2006. From his retirement in 2010 until now, he has been Professor Emeritus at the University of Savoy. His main research topics relate to differential geometry, dynamic systems, control theory and mathematical physics in finite and infinite dimensions.
Fernand Pelletier began his career as a researcher at the University of Burgundy in 1970. He obtained his third cycle doctorate in 1973 and his habilitation in 1980 at this University. Appointed Professor at the University of Corsica Pasquale Paoli in 1983, he was transferred to the University of Savoy in 1986. He was the Director of the Mathematics Laboratory (LAMA) of the University of Savoy from 1989 to 1996, Director of differential geometry teams in LAMA from 1996 to 2002 and Director of the "South Rodhanian" research group from 2002 to 2006. From his retirement in 2010 until now, he has been Professor Emeritus at the University of Savoy. His main research topics relate to differential geometry, dynamic systems, control theory and mathematical physics in finite and infinite dimensions.
Content
1. Preliminaries. 2. Banach Lie structures. 3. Convenient structures. 4. Projective limits. 5. Direct limits. 6. Convenient Lie algebroids and prolongations. 7. Partial Poisson structures. 8. Integrability of distributions.