Math Matiques L2
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Introduction To L2 Invariants
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Author : Holger Kammeyer
language : en
Publisher: Springer Nature
Release Date : 2019-10-29
Introduction To L2 Invariants written by Holger Kammeyer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Mathematics categories.
This book introduces the reader to the most important concepts and problems in the field of l2-invariants. After some foundational material on group von Neumann algebras, l2-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of l2-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of l2-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with l2-torsion, twisted variants and the conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.
L2 Invariants Theory And Applications To Geometry And K Theory
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Author : Wolfgang Lück
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
L2 Invariants Theory And Applications To Geometry And K Theory written by Wolfgang Lück and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Math Matiques L2
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Author : Jean-Pierre Marco
language : fr
Publisher: Pearson
Release Date : 2007-09-19
Math Matiques L2 written by Jean-Pierre Marco and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-19 with categories.
Mathématiques L2 est le second tome d'une série couvrant les besoins des étudiants préparant la licence de mathématiques ou le Capes de mathématiques. Il regroupe tout ce qui est nécessaire en L2 : un cours complet et détaillé ( algèbre, analyse, calcul différentiel, probabilités) et 700 tests et exercices entièrement corrigés. Il renferme également beaucoup d'éléments utiles à la préparation de l'agrégation de mathématiques.
Strong Limit Theorems In Noncommutative L2 Spaces
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Author : Ryszard Jajte
language : en
Publisher: Springer
Release Date : 2006-12-08
Strong Limit Theorems In Noncommutative L2 Spaces written by Ryszard Jajte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.
Fcs Mathematics L2
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Author :
language : en
Publisher: Pearson South Africa
Release Date :
Fcs Mathematics L2 written by and has been published by Pearson South Africa this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
L2 Approaches In Several Complex Variables
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Author : Takeo Ohsawa
language : en
Publisher: Springer
Release Date : 2015-09-28
L2 Approaches In Several Complex Variables written by Takeo Ohsawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-28 with Mathematics categories.
The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L2 extension of holomorphic functions. In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L2 method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L2 extension theorem with an optimal constant is included, obtained recently by Z. Błocki and by Q.-A. Guan and X.-Y. Zhou separately. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, and Guan–Zhou. Most of these results are obtained by the L2 method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L2 method obtained during these 15 years.
L2 Approaches In Several Complex Variables
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Author : Takeo Ohsawa
language : en
Publisher: Springer
Release Date : 2018-11-28
L2 Approaches In Several Complex Variables written by Takeo Ohsawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.
This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L2 extension of holomorphic functions in the past 5 years.In Chapter 1, the classical questions of several complex variables motivating the development of this field are reviewed after necessary preparations from the basic notions of those variables and of complex manifolds such as holomorphic functions, pseudoconvexity, differential forms, and cohomology. In Chapter 2, the L2 method of solving the d-bar equation is presented emphasizing its differential geometric aspect. In Chapter 3, a refinement of the Oka–Cartan theory is given by this method. The L2 extension theorem with an optimal constant is included, obtained recently by Z. Błocki and separately by Q.-A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L2 method. In the last chapter, rather specific results are discussed on the existence and classification of certain holomorphic foliations and Levi flat hypersurfaces as their stables sets. These are also applications of the L2 method obtained during the past 15 years.
Maths For Schools L2 Answers
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Author : Addison
language : en
Publisher:
Release Date : 1985-07-01
Maths For Schools L2 Answers written by Addison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-07-01 with categories.
Ergodic Theoretic Methods In Group Homology
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Author : Clara Löh
language : en
Publisher: Springer Nature
Release Date : 2020-03-14
Ergodic Theoretic Methods In Group Homology written by Clara Löh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-14 with Mathematics categories.
This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of L2-Betti numbers. Group homology integrates group actions into homological structure. Coefficients based on probability measure preserving actions combine ergodic theory and homology. An example of such an interaction is provided by L2-Betti numbers: these invariants can be understood in terms of group homology with coefficients related to the group von Neumann algebra, via approximation by finite index subgroups, or via dynamical systems. In this way, L2-Betti numbers lead to orbit/measure equivalence invariants and measured group theory helps to compute L2-Betti numbers. Similar methods apply also to compute the rank gradient/cost of groups as well as the simplicial volume of manifolds. This book introduces L2-Betti numbers of groups at an elementary level and then develops the ergodic point of view, emphasising the connection with approximation phenomena for homological gradient invariants of groups and spaces. The text is an extended version of the lecture notes for a minicourse at the MSRI summer graduate school “Random and arithmetic structures in topology” and thus accessible to the graduate or advanced undergraduate students. Many examples and exercises illustrate the material.
Szeg S Theorem And Its Descendants
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Author : Barry Simon
language : en
Publisher: Princeton University Press
Release Date : 2010-11-08
Szeg S Theorem And Its Descendants written by Barry Simon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-08 with Mathematics categories.
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.