Lie Groups Convex Cones And Semigroups

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Lie Groups, Convex Cones, and Semigroups

Author : Joachim Hilgert
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis Lie Groups, Convex Cones, and Semigroups by : Joachim Hilgert

Download or read book Lie Groups, Convex Cones, and Semigroups written by Joachim Hilgert and published by Oxford University Press, USA. This book was released on 1989 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first and only reference to provide a comprehensive treatment of the Lie theory of subsemigroups of Lie groups. The book is uniquely accessible and requires little specialized knowledge. It includes information on the infinitesimal theory of Lie subsemigroups, and a characterization of those cones in a Lie algebra which are invariant under the action of the group of inner automporphisms. It provides full treatment of the local Lie theory for semigroups, and finally, gives the reader a useful account of the global theory for the existence of subsemigroups with a given set of infinitesimal generators.

Lie Semigroups and their Applications

Author : Joachim Hilgert
Publisher : Springer
ISBN 13 : 3540699872
Total Pages : 327 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Lie Semigroups and their Applications by : Joachim Hilgert

Download or read book Lie Semigroups and their Applications written by Joachim Hilgert and published by Springer. This book was released on 2006-11-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subsemigroups of finite-dimensional Lie groups that are generated by one-parameter semigroups are the subject of this book. It covers basic Lie theory for such semigroups and some closely related topics. These include ordered homogeneous manifolds, where the order is defined by a field of cones, invariant cones in Lie algebras and associated Ol'shanskii semigroups. Applications to representation theory, symplectic geometry and Hardy spaces are also given. The book is written as an efficient guide for those interested in subsemigroups of Lie groups and their applications in various fields of mathematics (see the User's guide at the end of the Introduction). Since it is essentially self-contained and leads directly to the core of the theory, the first part of the book can also serve as an introduction to the subject. The reader is merely expected to be familiar with the basic theory of Lie groups and Lie algebras.

Semigroups in Algebra, Geometry and Analysis

Author : Karl H. Hofmann
Publisher : Walter de Gruyter
ISBN 13 : 3110885581
Total Pages : 385 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Semigroups in Algebra, Geometry and Analysis by : Karl H. Hofmann

Download or read book Semigroups in Algebra, Geometry and Analysis written by Karl H. Hofmann and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Holomorphy and Convexity in Lie Theory

Author : Karl-Hermann Neeb
Publisher : Walter de Gruyter
ISBN 13 : 3110808145
Total Pages : 804 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Holomorphy and Convexity in Lie Theory by : Karl-Hermann Neeb

Download or read book Holomorphy and Convexity in Lie Theory written by Karl-Hermann Neeb and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

The Analytical and Topological Theory of Semigroups

Author : Karl H. Hofmann
Publisher : Walter de Gruyter
ISBN 13 : 3110856042
Total Pages : 413 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis The Analytical and Topological Theory of Semigroups by : Karl H. Hofmann

Download or read book The Analytical and Topological Theory of Semigroups written by Karl H. Hofmann and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Quantization and Infinite-Dimensional Systems

Author : S.T. Ali
Publisher : Springer Science & Business Media
ISBN 13 : 1461525640
Total Pages : 273 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Quantization and Infinite-Dimensional Systems by : S.T. Ali

Download or read book Quantization and Infinite-Dimensional Systems written by S.T. Ali and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day.

Invariant Subsemigroups of Lie Groups

Author : Karl-Hermann Neeb
Publisher : American Mathematical Soc.
ISBN 13 : 0821825623
Total Pages : 209 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Invariant Subsemigroups of Lie Groups by : Karl-Hermann Neeb

Download or read book Invariant Subsemigroups of Lie Groups written by Karl-Hermann Neeb and published by American Mathematical Soc.. This book was released on 1993 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: First we investigate the structure of Lie algebras with invariant cones and give a characterization of those Lie algebras containing pointed and generating invariant cones. Then we study the global structure of invariant Lie semigroups, and how far Lie's third theorem remains true for invariant cones and Lie semigroups.

Differential Geometry and Control

Author : Guillermo Segundo Ferreyra
Publisher : American Mathematical Soc.
ISBN 13 : 0821808877
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Geometry and Control by : Guillermo Segundo Ferreyra

Download or read book Differential Geometry and Control written by Guillermo Segundo Ferreyra and published by American Mathematical Soc.. This book was released on 1999 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains papers from a summer 1997 meeting on recent developments and important open problems in geometric control theory. Topics include linear control systems in Lie groups and controllability, real analytic geometry and local observability, singular extremals of order 3 and chattering, infinite time horizon stochastic control problems in hyperbolic three space, and Monge-Ampere equations. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

The Lie Theory of Connected Pro-Lie Groups

Author : Karl Heinrich Hofmann
Publisher : European Mathematical Society
ISBN 13 : 9783037190326
Total Pages : 704 pages
Book Rating : 4.1/5 (93 download)

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Book Synopsis The Lie Theory of Connected Pro-Lie Groups by : Karl Heinrich Hofmann

Download or read book The Lie Theory of Connected Pro-Lie Groups written by Karl Heinrich Hofmann and published by European Mathematical Society. This book was released on 2007 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonne quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a pro-Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of pro-Lie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinite-dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite-dimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected pro-Lie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finite-dimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics.

Positive Definite Functions on Infinite-Dimensional Convex Cones

Author : Helge Glöckner
Publisher : American Mathematical Soc.
ISBN 13 : 0821832565
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Positive Definite Functions on Infinite-Dimensional Convex Cones by : Helge Glöckner

Download or read book Positive Definite Functions on Infinite-Dimensional Convex Cones written by Helge Glöckner and published by American Mathematical Soc.. This book was released on 2003 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.

Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs

Author : Elemer E. Rosinger
Publisher : Springer Science & Business Media
ISBN 13 : 9401590761
Total Pages : 247 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs by : Elemer E. Rosinger

Download or read book Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs written by Elemer E. Rosinger and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents global actions of arbitrary Lie groups on large classes of generalised functions by using a novel parametric approach. This new method extends and completes earlier results of the author and collaborators, in which global Lie group actions on generalised functions were only defined in the case of projectable or fibre-preserving Lie group actions. The parametric method opens the possibility of dealing with vastly larger classes of Lie semigroup actions which still transform solutions into solutions. These Lie semigroups can contain arbitrary noninvertible smooth mappings. Thus, they cannot be subsemigroups of Lie groups. Audience: This volume is addressed to graduate students and researchers involved in solving linear and nonlinear partial differential equations, and in particular, in dealing with the Lie group symmetries of their classical or generalised solutions.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512353
Total Pages : 549 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Infinite Dimensional Harmonic Analysis Iv: On The Interplay Between Representation Theory, Random Matrices, Special Functions, And Probability - Proceedings Of The Fourth German-japanese Symposium

Download Infinite Dimensional Harmonic Analysis Iv: On The Interplay Between Representation Theory, Random Matrices, Special Functions, And Probability - Proceedings Of The Fourth German-japanese Symposium PDF Online Free

Author : Joachim Hilgert
Publisher : World Scientific
ISBN 13 : 9814470449
Total Pages : 337 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Infinite Dimensional Harmonic Analysis Iv: On The Interplay Between Representation Theory, Random Matrices, Special Functions, And Probability - Proceedings Of The Fourth German-japanese Symposium by : Joachim Hilgert

Download or read book Infinite Dimensional Harmonic Analysis Iv: On The Interplay Between Representation Theory, Random Matrices, Special Functions, And Probability - Proceedings Of The Fourth German-japanese Symposium written by Joachim Hilgert and published by World Scientific. This book was released on 2008-11-26 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.

Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV

Author : Joachim Hilgert
Publisher : World Scientific
ISBN 13 : 9812832815
Total Pages : 337 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV by : Joachim Hilgert

Download or read book Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV written by Joachim Hilgert and published by World Scientific. This book was released on 2009 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.

Lie Groups and Subsemigroups with Surjective Exponential Function

Author : Karl Heinrich Hofmann
Publisher : American Mathematical Soc.
ISBN 13 : 0821806416
Total Pages : 189 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Groups and Subsemigroups with Surjective Exponential Function by : Karl Heinrich Hofmann

Download or read book Lie Groups and Subsemigroups with Surjective Exponential Function written by Karl Heinrich Hofmann and published by American Mathematical Soc.. This book was released on 1997 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

Causal Symmetric Spaces

Author : Gestur Olafsson
Publisher : Academic Press
ISBN 13 : 0080528724
Total Pages : 303 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Causal Symmetric Spaces by : Gestur Olafsson

Download or read book Causal Symmetric Spaces written by Gestur Olafsson and published by Academic Press. This book was released on 1996-09-11 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces

Geometric Control and Non-holonomic Mechanics

Author : Velimir Jurdjevic
Publisher : American Mathematical Soc.
ISBN 13 : 9780821807958
Total Pages : 256 pages
Book Rating : 4.8/5 (79 download)

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Book Synopsis Geometric Control and Non-holonomic Mechanics by : Velimir Jurdjevic

Download or read book Geometric Control and Non-holonomic Mechanics written by Velimir Jurdjevic and published by American Mathematical Soc.. This book was released on 1998 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control theory, a synthesis of geometric theory of differential equations enriched with variational principles and the associated symplectic geometry, emerges as a new mathematical subject of interest to engineers, mathematicians, and physicists. This collection of articles focuses on several distinctive research directions having origins in mechanics and differential geometry, but driven by modern control theory. The first of these directions deals with the singularities of small balls for problems of sub-Riemannian geomtery and provides a generic classification of singularities for two-dimensional distributions of contact type in a three-dimensional ambient space. The second direction deals with invariant optimal problems on Lie groups exemplified through the problem of Dublins extended to symmetric spaces, the elastic problem of Kirchhoff and its relation to the heavy top. The results described in the book are explicit and demonstrate convincingly the power of geometric formalism. The remaining directions deal with the geometric nature of feedback analysed through the language of fiber bundles, and the connections of geometric control to non-holonomic problems in mechanics, as exemplified through the motions of a sphere on surfaces of revolution. This book provides quick access to new research directions in geometric control theory. It also demonstrates the effectiveness of new insights and methods that control theory brings to mechanics and geometry.