Harmonic Analysis On Exponential Solvable Lie Groups

Author : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 465 pages
File Size : 54,9 Mb
Release : 2015-01-10
Category : Mathematics
ISBN : 4431552898

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Harmonic Analysis on Exponential Solvable Lie Groups by Hidenori Fujiwara,Jean Ludwig Pdf

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.

Author : Hidenori Fujiwara,Jean Ludwig
Publisher : Springer
Page : 468 pages
File Size : 42,6 Mb
Release : 2014-12-05
Category : Mathematics
ISBN : 9784431552888

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Harmonic Analysis on Exponential Solvable Lie Groups by Hidenori Fujiwara,Jean Ludwig Pdf

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.

Author : Ali Baklouti,Hidenori Fujiwara,Jean Ludwig
Publisher : Springer Nature
Page : 620 pages
File Size : 42,7 Mb
Release : 2021-10-08
Category : Mathematics
ISBN : 9783030820442

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Representation Theory of Solvable Lie Groups and Related Topics by Ali Baklouti,Hidenori Fujiwara,Jean Ludwig Pdf

The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.

Author : Ali Baklouti,Hideyuki Ishi
Publisher : Springer Nature
Page : 268 pages
File Size : 50,6 Mb
Release : 2021-10-29
Category : Mathematics
ISBN : 9783030783464

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Geometric and Harmonic Analysis on Homogeneous Spaces and Applications by Ali Baklouti,Hideyuki Ishi Pdf

This book collects a series of important works on noncommutative harmonic analysis on homogeneous spaces and related topics. All the authors participated in the 6th Tunisian-Japanese conference "Geometric and Harmonic Analysis on homogeneous spaces and Applications" held at Djerba Island in Tunisia during the period of December 16-19, 2019. The aim of this conference and the five preceding Tunisian-Japanese meetings was to keep up with the active development of representation theory interrelated with various other mathematical fields, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations, and mathematical physics. The present volume is dedicated to the memory of Takaaki Nomura, who organized the series of Tunisian-Japanese conferences with great effort and enthusiasm. The book is a valuable resource for researchers and students working in various areas of analysis, geometry, and algebra in connection with representation theory.

Author : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 463 pages
File Size : 43,7 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108428095

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Representations of Solvable Lie Groups and their Applications by Didier Arnal,Bradley Currey Pdf

A complete and self-contained account of the basic theory of unitary group representations for graduate students and researchers.

Author : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 464 pages
File Size : 43,9 Mb
Release : 2020-04-08
Category : Mathematics
ISBN : 9781108651936

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Representations of Solvable Lie Groups by Didier Arnal,Bradley Currey Pdf

The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.

Author : Ali Baklouti,Takaaki Nomura
Publisher : Springer Nature
Page : 217 pages
File Size : 51,7 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9783030265625

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Geometric and Harmonic Analysis on Homogeneous Spaces by Ali Baklouti,Takaaki Nomura Pdf

This book presents a number of important contributions focusing on harmonic analysis and representation theory of Lie groups. All were originally presented at the 5th Tunisian–Japanese conference “Geometric and Harmonic Analysis on Homogeneous Spaces and Applications”, which was held at Mahdia in Tunisia from 17 to 21 December 2017 and was dedicated to the memory of the brilliant Tunisian mathematician Majdi Ben Halima. The peer-reviewed contributions selected for publication have been modified and are, without exception, of a standard equivalent to that in leading mathematical periodicals. Highlighting the close links between group representation theory and harmonic analysis on homogeneous spaces and numerous mathematical areas, such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics, the book is intended for researchers and students working in the area of commutative and non-commutative harmonic analysis as well as group representations.

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662030028

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Representation Theory and Noncommutative Harmonic Analysis I by A.A. Kirillov Pdf

This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

Author : J. Carmona,M. Vergne
Publisher : Springer
Page : 562 pages
File Size : 50,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387831

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Non Commutative Harmonic Analysis and Lie Groups by J. Carmona,M. Vergne Pdf

Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 40,9 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821815236

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Noncommutative Harmonic Analysis by Michael Eugene Taylor Pdf

Explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations.

Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 46,7 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781498727150

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A Course in Abstract Harmonic Analysis by Gerald B. Folland Pdf

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 50,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821803004

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Representation Theory and Analysis on Homogeneous Spaces by Semen Grigorʹevich Gindikin Pdf

A combination of new results and surveys of recent work on representation theory and the harmonic analysis of real and p-adic groups. Among the topics are nilpotent homogeneous spaces, multiplicity formulas for induced representations, and new methods for constructing unitary representations of real reductive groups. The 12 papers are from a conference at Rutgers University, February 1993. No index. Annotation copyright by Book News, Inc., Portland, OR

Author : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662097564

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Representation Theory and Noncommutative Harmonic Analysis II by A.A. Kirillov Pdf

Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.

Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642516405

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Harmonic Analysis on Semi-Simple Lie Groups II by Garth Warner Pdf

Author : Nick Dungey,A.F.M. (Tom) ter Elst,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220626

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Analysis on Lie Groups with Polynomial Growth by Nick Dungey,A.F.M. (Tom) ter Elst,Derek William Robinson Pdf

Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one. This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory.