WorldCat Identities

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
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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 self-contained 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 C-algebra 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

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 spectral-theoretic 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 eigenvalue-spectrum of the transfer operator, isospectral families of wavelets, spectral radius formulas for the transfer operator, Perron-Frobenius 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 self-contained 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

Representation theory and numerical AF-invariants : 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 AF-invariants 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 3-5, 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 "non-commutative geometry" (see for example the book "Non-Commutative Geometry" by the Fields medalist Alain Connes). It has branched out in several sub-disciplines 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 state-of-the-art account of some of these sub-disciplines 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 non-commutative 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 Fokker-Planck 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 Batty-Robinson 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 sub-divisions
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

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
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

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

Operator algebras and quantum statistical mechanics by Ola Bratteli( Book )

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

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

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

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

Operator algebras and quantum statistical mechanics by Ola Bratteli( )

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

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

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 "non-commutative geometry."
 
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Audience level: 0.68 (from 0.53 for Operator a ... to 0.98 for Operator a ...)

Derivations, dissipations, and group actions on C*-algebras
Alternative Names
Bratelli, Ola

Bratteli, O.

Bratteli, Ola

Bratteli, U.

Ola Bratteli Noors wiskundige (1946-2015)

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
English (213)

Russian (5)

Italian (2)

German (1)

Covers
Derivations, dissipations, and group actions on C*-algebrasWavelets through a looking glass : the world of the spectrumIterated function systems and permutation representations of the Cuntz algebraOperator algebras : the Abel Symposium 2004 : proceedings of the First Abel Symposium, Oslo, September 3-5, 2004Positive semigroups of operators, and applicationsC*- and W*-Algebras, symmetry groups, decomposition of stateEquilibrium states, models in quantum statistical mechanicsOperator algebras and quantum statistical mechanics