Bratteli, Ola
Overview
Works:  90 works in 281 publications in 4 languages and 2,927 library holdings 

Genres:  Conference 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
)
33 editions published between 1979 and 2002 in 3 languages and held by 544 WorldCat member libraries worldwide
33 editions published between 1979 and 2002 in 3 languages and held by 544 WorldCat member libraries worldwide
Derivations, dissipations, and group actions on C*algebras by
Ola Bratteli(
Book
)
26 editions published between 1986 and 2008 in 3 languages and held by 371 WorldCat member libraries worldwide
26 editions published between 1986 and 2008 in 3 languages and held by 371 WorldCat member libraries worldwide
Wavelets through a looking glass : the world of the spectrum by
Ola Bratteli(
Book
)
9 editions published between 2002 and 2014 in English and held by 318 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radius formulas for the transfer operator, PerronFrobenius theory, and quadrature mirror filters * New previously unpublished results appear on the homotopy of multiresolutions, on approximation theory, and on the spectrum and structure of the fixed points of the associated transfer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
9 editions published between 2002 and 2014 in English and held by 318 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
)
13 editions published in 1999 in English and held by 229 WorldCat member libraries worldwide
13 editions published in 1999 in English and held by 229 WorldCat member libraries worldwide
Representation theory and numerical AFinvariants : the representations and centralizers of certain states on Od by
Ola Bratteli(
Book
)
12 editions published in 2004 in English and held by 223 WorldCat member libraries worldwide
12 editions published in 2004 in English and held by 223 WorldCat member libraries worldwide
Operator algebras and quantum statistical mechanics 2 : Equilibrium states. Models in quantum statistical mechanics by
Ola Bratteli(
Book
)
35 editions published between 1981 and 2011 in 3 languages and held by 156 WorldCat member libraries worldwide
35 editions published between 1981 and 2011 in 3 languages and held by 156 WorldCat member libraries worldwide
Operator algebras : the Abel Symposium 2004 : proceedings of the First Abel Symposium, Oslo, September 35, 2004 by
Ola Bratteli(
Book
)
20 editions published in 2006 in English and held by 127 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
20 editions published in 2006 in English and held by 127 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 68 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 68 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
Equilibrium states, models in quantum statistical mechanics by
Ola Bratteli(
Book
)
1 edition published in 1997 in English and held by 10 WorldCat member libraries worldwide
Band 2
1 edition published in 1997 in English and held by 10 WorldCat member libraries worldwide
Band 2
Operatornye algebry i kvantovaja statističeskaja mechanika : C* i W*algebry gruppy simmetrij razloženie sostojanij by
Ola Bratteli(
Book
)
3 editions published in 1982 in Russian and held by 8 WorldCat member libraries worldwide
3 editions published in 1982 in Russian and held by 8 WorldCat member libraries worldwide
C* and W*algebras, symmetry groups, decomposition of states by
Ola Bratteli(
Book
)
1 edition published in 1979 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1979 in English and held by 6 WorldCat member libraries worldwide
Operator algebras proceedings of the First Abel Symposium, Oslo, September 3  5, 2004(
Book
)
2 editions published in 2006 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 6 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
C* and W*Algebras, symmetry groups, decomposition of state by
Ola Bratteli(
Book
)
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
)
2 editions published between 1979 and 2002 in English and held by 6 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
2 editions published between 1979 and 2002 in English and held by 6 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
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
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
Relative locality of derivations by
Ola Bratteli(
Book
)
4 editions published in 1983 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1983 in English and held by 4 WorldCat member libraries worldwide
Operator Algebras Volume 1, The Abel Symposium 2004 by
Ola Bratteli(
)
1 edition 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."
1 edition 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."
Operator algebras and quantum statistical mechanics equilibrium states. Models in quantum statistical mechanics by
Ola Bratteli(
)
2 editions published between 1981 and 1997 in English and held by 0 WorldCat member libraries worldwide
For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMScondition and stability, quantum spin systems and continuous systems. Major changes in the new edition relate to BoseEinstein condensation, the dynamics of the XY model and questions on phase transitions. Notes and remarks have been considerably augmented
2 editions published between 1981 and 1997 in English and held by 0 WorldCat member libraries worldwide
For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMScondition and stability, quantum spin systems and continuous systems. Major changes in the new edition relate to BoseEinstein condensation, the dynamics of the XY model and questions on phase transitions. Notes and remarks have been considerably augmented
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C*algebras Differentiable dynamical systems Ergodic theory Fourier analysis Functional analysis Global analysis (Mathematics) Group theory Harmonic analysis Hilbert space Ktheory Linear operators Mathematical physics Mathematics Noncommutative algebras Operator algebras Operator theory Physics Quantum statistics Representations of groups Selfadjoint operators Semigroups of operators Spectral theory (Mathematics) Statistical mechanics Topological groups Von Neumann algebras Wavelets (Mathematics)
Alternative Names
Bratelli, Ola
Bratteli, O.
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.
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