Bratteli, Ola
Overview
Works:  84 works in 316 publications in 4 languages and 3,197 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA326, 512.55 
Publication Timeline
.
Most widely held works by
Ola Bratteli
Operator algebras and quantum statistical mechanics by
Ola Bratteli(
Book
)
114 editions published between 1979 and 2011 in 3 languages and held by 851 WorldCat member libraries worldwide
This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is selfcontained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of Calgebra were automatically maximal along all the probability measures on the space
114 editions published between 1979 and 2011 in 3 languages and held by 851 WorldCat member libraries worldwide
This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is selfcontained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of Calgebra were automatically maximal along all the probability measures on the space
Derivations, dissipations, and group actions on C*algebras by
Ola Bratteli(
Book
)
22 editions published between 1986 and 2008 in 3 languages and held by 358 WorldCat member libraries worldwide
22 editions published between 1986 and 2008 in 3 languages and held by 358 WorldCat member libraries worldwide
Wavelets through a looking glass : the world of the spectrum by
Ola Bratteli(
Book
)
12 editions published between 2002 and 2014 in English and held by 321 WorldCat member libraries worldwide
This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectraltheoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. Key features of the book: The important role of the spectrum of a transfer operator is studied * Excellent graphics show how wavelets depend on the spectra of the transfer operators * Key topics of wavelet theory are examined: connected components in the variety of wavelets, the geometry of winding numbers, the Galerkin projection method, classical functions of Weierstrass and Hurwitz and their role in describing the eigenvaluespectrum of the transfer operator, isospectral families of wavelets, spectral radius formulas for the transfer operator, PerronFrobenius theory, and quadrature mirror filters * New previously unpublished results appear on the homotopy of multiresolutions, on approximation theory, and on the spectrum and structure of the fixed points of the associated transfer and subdivision operators * Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource. This selfcontained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory
12 editions published between 2002 and 2014 in English and held by 321 WorldCat member libraries worldwide
This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectraltheoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. Key features of the book: The important role of the spectrum of a transfer operator is studied * Excellent graphics show how wavelets depend on the spectra of the transfer operators * Key topics of wavelet theory are examined: connected components in the variety of wavelets, the geometry of winding numbers, the Galerkin projection method, classical functions of Weierstrass and Hurwitz and their role in describing the eigenvaluespectrum of the transfer operator, isospectral families of wavelets, spectral radius formulas for the transfer operator, PerronFrobenius theory, and quadrature mirror filters * New previously unpublished results appear on the homotopy of multiresolutions, on approximation theory, and on the spectrum and structure of the fixed points of the associated transfer and subdivision operators * Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource. This selfcontained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory
Iterated function systems and permutation representations of the Cuntz algebra by
Ola Bratteli(
Book
)
11 editions published in 1999 in English and held by 225 WorldCat member libraries worldwide
11 editions published in 1999 in English and held by 225 WorldCat member libraries worldwide
Representation theory and numerical AFinvariants : the representations and centralizers of certain states on Od by
Ola Bratteli(
Book
)
1 edition published in 2004 in English and held by 200 WorldCat member libraries worldwide
Part A. Representation theory Part B. Numerical AFinvariants Bibliography List of figures List of tables List of terms and symbols
1 edition published in 2004 in English and held by 200 WorldCat member libraries worldwide
Part A. Representation theory Part B. Numerical AFinvariants Bibliography List of figures List of tables List of terms and symbols
Operator algebras : the Abel Symposium 2004 : proceedings of the First Abel Symposium, Oslo, September 35, 2004 by
Ola Bratteli(
Book
)
22 editions published in 2006 in English and held by 135 WorldCat member libraries worldwide
The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis pline within functional analysis to become a central ?eld in mathematics often described as "noncommutative geometry" (see for example the book "NonCommutative Geometry" by the Fields medalist Alain Connes). It has branched out in several subdisciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a stateoftheart account of some of these subdisciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ?eld were willing to contribute. The basic ?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite  mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral  erators. An important feature is that the composition of two operators is a noncommutative operation
22 editions published in 2006 in English and held by 135 WorldCat member libraries worldwide
The theme of this symposium was operator algebras in a wide sense. In the last 40 years operator algebras has developed from a rather special dis pline within functional analysis to become a central ?eld in mathematics often described as "noncommutative geometry" (see for example the book "NonCommutative Geometry" by the Fields medalist Alain Connes). It has branched out in several subdisciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dyn ical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the ?rst symposium in the series of Abel Symposia to this group. The contributions to this volume give a stateoftheart account of some of these subdisciplines and the variety of topics re?ect to some extent how the subject has branched out. We are happy that some of the top researchers in the ?eld were willing to contribute. The basic ?eld of operator algebras is classi?ed within mathematics as part of functional analysis. Functional analysis treats analysis on in?nite  mensional spaces by using topological concepts. A linear map between two such spaces is called an operator. Examples are di?erential and integral  erators. An important feature is that the composition of two operators is a noncommutative operation
Positive semigroups of operators, and applications by
Ola Bratteli(
Book
)
11 editions published in 1984 in English and Undetermined and held by 70 WorldCat member libraries worldwide
This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1 <p <00. From this, Yau gets the geometric fact that complete noncom pact Riemannian manifolds with nonnegative Ricci curvature must have infinite volume, a result which was announced earlier by Calabi [4]. 6. Concluding Remarks In several of the above results, positivity of the semigroup plays an important role. This was also true, although only implicitly, for the early work of Hille and Yosida on the FokkerPlanck equation, i.e., Equation (4) with c = O. But it was Phillips [41], and Lumer and Phillips [37] who first called attention to the importance of dissipative and dispersive properties of the generator in the context of linear operators in a Banach space. The generation theorems in the BattyRobinson paper appear to be the most definitive ones, so far, for this class of operators. The fundamental role played by the infinitesimal operator, also for the understanding of order properties, in the commutative as well as the noncommutative setting, are highlighted in a number of examples and applications in the different papers, and it is hoped that this publication will be of interest to researchers in a broad spectrum of the mathematical subdivisions
11 editions published in 1984 in English and Undetermined and held by 70 WorldCat member libraries worldwide
This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1 <p <00. From this, Yau gets the geometric fact that complete noncom pact Riemannian manifolds with nonnegative Ricci curvature must have infinite volume, a result which was announced earlier by Calabi [4]. 6. Concluding Remarks In several of the above results, positivity of the semigroup plays an important role. This was also true, although only implicitly, for the early work of Hille and Yosida on the FokkerPlanck equation, i.e., Equation (4) with c = O. But it was Phillips [41], and Lumer and Phillips [37] who first called attention to the importance of dissipative and dispersive properties of the generator in the context of linear operators in a Banach space. The generation theorems in the BattyRobinson paper appear to be the most definitive ones, so far, for this class of operators. The fundamental role played by the infinitesimal operator, also for the understanding of order properties, in the commutative as well as the noncommutative setting, are highlighted in a number of examples and applications in the different papers, and it is hoped that this publication will be of interest to researchers in a broad spectrum of the mathematical subdivisions
C* and W*Algebras, symmetry groups, decomposition of state by
Ola Bratteli(
Book
)
2 editions published between 1979 and 2002 in English and held by 12 WorldCat member libraries worldwide
2 editions published between 1979 and 2002 in English and held by 12 WorldCat member libraries worldwide
Equilibrium states, models in quantum statistical mechanics by
Ola Bratteli(
Book
)
2 editions published between 1981 and 1997 in English and held by 11 WorldCat member libraries worldwide
Band 2
2 editions published between 1981 and 1997 in English and held by 11 WorldCat member libraries worldwide
Band 2
Operator algebras and quantum statistical mechanics by
Ola Bratteli(
Book
)
2 editions published in 1979 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1979 in English and held by 7 WorldCat member libraries worldwide
Wavelets through a looking glass the world of the spectrum by
Ola Bratteli(
Visual
)
1 edition published in 2002 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 6 WorldCat member libraries worldwide
Operator algebras and quantum statistical mechanics by
Ola Bratteli(
Book
)
in English and held by 6 WorldCat member libraries worldwide
in English and held by 6 WorldCat member libraries worldwide
Subelliptic operators on Lie groups : variable coefficients by
Ola Bratteli(
Book
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Abundance of invariant and almost invariant pure states of C*dynamical systems by
Ola Bratteli(
Book
)
3 editions published in 1996 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 5 WorldCat member libraries worldwide
Spectral asymptotics of periodic elliptic operators by
Ola Bratteli(
Book
)
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Unbounded derivations tangential to compact groups of automorphisms by
Ola Bratteli(
Book
)
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
Operator algebras and quantum statistical mechanics by
Ola Bratteli(
)
in Undetermined and English and held by 4 WorldCat member libraries worldwide
in Undetermined and English and held by 4 WorldCat member libraries worldwide
Approximately finite dimensional c*algebras by
Ola Bratteli(
Book
)
5 editions published between 1974 and 1978 in English and held by 4 WorldCat member libraries worldwide
5 editions published between 1974 and 1978 in English and held by 4 WorldCat member libraries worldwide
Iterated function systems and permutations representations of the Cuntz algebra by
Ola Bratteli(
Book
)
3 editions published between 1996 and 1999 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1996 and 1999 in English and held by 3 WorldCat member libraries worldwide
Operator Algebras : the Abel Symposium 2004 00 by
Ola Bratteli(
)
3 editions published in 2006 in English and held by 0 WorldCat member libraries worldwide
Part of a book series linked to the Abel prize, this book the theme of the first Abel Symposium  operator algebras. Operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "noncommutative geometry."
3 editions published in 2006 in English and held by 0 WorldCat member libraries worldwide
Part of a book series linked to the Abel prize, this book the theme of the first Abel Symposium  operator algebras. Operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "noncommutative geometry."
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Robinson, Derek W.
 Jørgensen, Palle E. T. 1947 Other Editor
 Skau, Christian Editor
 Neshveyev, Sergey Editor
 Ostrovsʹkyĭ, Vasylʹ
 SpringerLink (Service en ligne)
 Kishimoto, Akitaka
 Treadway, Brian Illustrator
 Australian National University School of Mathematical Sciences
 Abel Symposium (1, 2004, Oslo)
Useful Links
Associated Subjects
C*algebras Computer engineering Differentiable dynamical systems Differential equations, Hypoelliptic Electronic data processing Elliptic operators Ergodic theory Fourier analysis Functional analysis Functions, Orthogonal Global analysis (Mathematics) Group theory Harmonic analysis Hilbert space Ktheory Lie groups Linear operators Mathematical physics Mathematics Nilpotent Lie groups Noncommutative algebras Operator algebras Operator theory Orthogonal polynomials Physics Quantum statistics Representations of groups Selfadjoint operators Semigroups of operators Solvable groups Spectral sequences (Mathematics) Spectral theory (Mathematics) Statistical mechanics Topological groups Von Neumann algebras Wavelets (Mathematics)
Alternative Names
Bratelli, Ola
Bratteli, O.
Bratteli, Ola
Bratteli, U.
Ola Bratteli Noors wiskundige (19462015)
Ola Bratteli norsk matematikar og professor
Ola Bratteli norsk matematiker og professor
Ola Bratteli Norwegian mathematician and professor
Ola Bratteli norwegischer Mathematiker
Браттели, У.
Languages
Covers