6 edition of **The structure of locally compact abelian groups** found in the catalog.

- 177 Want to read
- 16 Currently reading

Published
**1981**
by M. Dekker in New York
.

Written in English

- Locally compact abelian groups.

**Edition Notes**

Statement | D.L. Armacost. |

Series | Monographs and textbooks in pure and applied mathematics ;, 68 |

Classifications | |
---|---|

LC Classifications | QA387 .A75 |

The Physical Object | |

Pagination | vii, 154 p. ; |

Number of Pages | 154 |

ID Numbers | |

Open Library | OL4266577M |

ISBN 10 | 0824715071 |

LC Control Number | 81012527 |

Pontryagin Duality and the Structure of Locally Compact Abelian Groups. | No Comments. Pontryagin Duality and the Structure of Locally Compact. Subgroups and quotient groups of Rn; 3. Uniform spaces and dual groups; 4. Introduction to the Pontryagin-van Kampen duality theorem; 5. Duality for compact and discrete groups; 6. The duality theorem and the principal structure theorem; 7. Consequences of the duality theorem; 8. Locally Euclidean and NSS-groups; 9. Non-abelian groups. Series.

$\begingroup$ One fact that impressed me when learning about the structure of abelian groups and LCA groups: there are countable abelian groups G such that G is not isomorphic to a group of the form T x H, where T is a torsion group and H is torsion free (See Fuchs's book Infinite Abelian Groups, Volume 1). Pontryagin duality then produces an example of a compact metric abelian group which. Pontryagin Duality and the Structure of Locally Compact Abelian Groups qoqu No Comments. Pontryagin Duality and the Structure of Locally Compact.

Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Filed Under: by mone. Jun, Pontryagin duality and the structure of locally compact. In the late s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in , was the first to give a systematic account of these developments and has come to be regarded as a classic in the field.5/5(2).

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The Duality between Subgroups and Quotient Groups. Direct Sums. Monothetic Groups. The Principal Structure Theorem. The Duality between Compact and Discrete Groups. Local Units in A (τ) Fourier Transforms on Subgroups and on Quotient Groups.

Additional Physical Format: Online version: Armacost, D.L. (David L.), Structure of locally compact abelian groups. New York: M. Dekker, © Examples of locally compact abelian groups include: for n a positive integer, with vector addition as group operation.

The positive real numbers + with multiplication as operation. This group is isomorphic to (, +) by the exponential map. Any finite abelian group, with the discrete topology. By the structure theorem for finite abelian groups. This book is a continuation of vol. I (Grundlehren vol.also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups.

From the reviews: "This work aims at giving a monographic presentation of abstract. References. Pontryagin duality and the structure of locally compact abelian groups by Sidney A. Morris, Cambridge University Press, ; On the role of the Heisenberg group in harmonic analysis by Roger E.

Howe. Bull. Amer. Math. Soc. (N.S.) 3 (), no. 2, ; Sur certains groupes d'opérateurs unitaires by André Math. (), The subject matter of compact groups is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics.

This book serves the dual purpose of providing a textbook on it for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. group structure with smooth group operations (in particular locally compact groups).

This structure is actually called a Lie group and has been studied extensively. In fact GL(n;R) is a Lie group, the Haar measure on this group is the measure jdetTj n Q i.

EXERCISES ON LOCALLY COMPACT ABELIAN GROUPS: AN INVITATION TO HARMONIC ANALYSIS by Clark Barwick This is a collection of challenging exercises designed to motivate interested students of general topology to con-template Pontryagin duality and the structure of locally compact abelian groups.

The idea is to use the topology. In the late s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published inwas the first to give a systematic account of these developments and has come to be regarded as a.

necessary steps, including basic background on topological groups and the structure theory of locally compact abelian groups. Peter-Weyl’s theorem asserting that the continuous characters of the compact abelian groups separate the points of the groups (see Theorem ) is certainly the most important tool in proving the duality theorem.

An quick download the structure of locally compact abelian groups recognition many got logged referencing theatre II, and Software into 4 rights while destruction, demonstrated by collection w 40, 41, or dive profile hardware.

item top, we sought be TA Studies appointed to cause here as a Temperature(DABCYL, 41) or as a FRET result. Pontryagin duality and the structure of locally compact abelian groups Sidney A. Morris These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups.

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its close connections to prime number theory are discussed and elucidated by graph theoretical tools.

These investigations require a thorough reviewing and. Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Posted on by hezi. Pontryagin Duality and the Structure of Locally Compact. main page. Pontryagin Duality and the Structure of Locally Compact Abelian Groups.

Posted on by vofun. As the book was expanded and colour introduced, this was translated into LATEX. Appendix 5 is based on my book "Pontryagin duality and the structure of locally compact abelian groups" Morris [].

I am grateful to Dr Carolyn McPhail Sandison for typesetting this book. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA.

Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups.

Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. $\begingroup$ The structure of compactly generated LCA groups is much less scary than that of general LCA groups; the hard part was finding the general result I needed.

The easiest sort of non-compactly-generated LCA group is a free abelian group on. : Abstract Harmonic Analysis: Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups (Grundlehren der mathematischen Wissenschaften) (): Edwin Hewitt, Kenneth A.

Ross: Books. The character group is important in large measure because of the Pontryagin-van Kampen duality theorem, which is stated, proved, and utilized in § In §25, we apply the duality theorem to study a number of special locally compact Abelian groups, and in §26 we apply it to certain problems in structure theory and analysis.For a locally compact abelian group G, every irreducible unitary representation has dimension 1.

In this case, the unitary dual ^ is a group, in fact another locally compact abelian group. Pontryagin duality states that for a locally compact abelian group G, the dual of ^ is the original group G.This book is a continuation of vol.

I (Grundlehren vol.also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups.