Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups PDF Download
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Author: Eberhard Kaniuth
Publisher: American Mathematical Soc.
ISBN: 0821853651
Category : Mathematics
Languages : en
Pages : 321
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Book Description
The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
Author: Eberhard Kaniuth
Publisher: American Mathematical Soc.
ISBN: 0821853651
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.
Author: Walter Rudin
Publisher: Courier Dover Publications
ISBN: 0486813657
Category : Mathematics
Languages : en
Pages : 305
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Book Description
Self-contained treatment by a master mathematical expositor ranges from introductory chapters on basic theorems of Fourier analysis and structure of locally compact Abelian groups to extensive appendixes on topology, topological groups, more. 1962 edition.
Author: Michel Enock
Publisher: Springer Science & Business Media
ISBN: 3662028131
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This book deals with the theory of Kac algebras and their dual ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. !. Kac and L. !. Vajnermann in the seventies. The sub ject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the character ization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. !. Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality.
Author: Loren N. Argabright
Publisher: American Mathematical Soc.
ISBN: 0821818457
Category : Abelian groups
Languages : en
Pages : 61
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Book Description
In harmonic analysis on a LCA group G, the term "Fourier transform" has a variety of meanings. It refers to various objects constructed in special ways, depending on the desired theory. The standard theories include the theory of Fourier-Stieltjes transforms, the Plancherel theorem, and the Bochner theorem can be viewed as another aspect of this phenomenon. However, except for special cases, we know of no attempt in the literature to undertake the desired synthesis. The purpose of the present work is to give a systematic account of such an attempt.
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Author: Brian Edmund Forrest
Publisher: National Library of Canada
ISBN:
Category : Locally compact groups
Languages : en
Pages : 186
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Book Description
Author: Kelly McKennon
Publisher: American Mathematical Soc.
ISBN: 0821818112
Category : Algebraic functions
Languages : en
Pages : 75
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Book Description
Author: Gero Fendler
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Laura Martí Pérez
Publisher:
ISBN:
Category :
Languages : en
Pages : 180
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Book Description
The goal of this thesis is to define and study the Fourier algebra A(G) of a locally compact groupoid G. If G is a locally compact group, its Fourier-Stieltjes algebra B(G) and its Fourier algebra A(G) were defined by Eymard in 1964. Since then, a rich theory has been developed. For the groupoid case, the algebras B(G) and A(G) have been studied by Ramsay and Walter (borelian case, 1997), Renault (measurable case, 1997) and Paterson (locally compact case, 2004). In this work, we present a new definition of A(G) in the locally compact case, specially well suited for studying locally trivial groupoids.
Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821847759
Category : Mathematics
Languages : en
Pages : 178
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Book Description
"Volume 205, number 966 (end of volume)."
Author: Anna Kamińska
Publisher: American Mathematical Soc.
ISBN: 0821832344
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.
