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This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

Discontinuous groups. --- Combinatorial topology --- Functions of complex variables --- Group theory

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This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry. Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces form a significant and important area of mathematical research. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics.  Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic, the first of which took place on November 2009 in Kerkennah Islands, the second in Sousse  on December 2011, and the third in Hammamet& nbsp;on December 2013. The last seminar, which took place on December 18th to 23rd 2015 in Monastir, Tunisia, has promoted further research in all the fields where the main focus was in the area of Analysis, algebra and geometry and on topics of joint collaboration of many teams in several corners. Many experts from both countries have been involved.

Geometry, Algebraic. --- Topological groups. --- Mathematics. --- Algebraic geometry. --- Lie groups. --- Harmonic analysis. --- Partial differential equations. --- Differential geometry. --- Number theory. --- Abstract Harmonic Analysis. --- Topological Groups, Lie Groups. --- Number Theory. --- Algebraic Geometry. --- Differential Geometry. --- Partial Differential Equations. --- Groups, Topological --- Continuous groups --- Algebraic geometry --- Geometry --- Topological Groups. --- Geometry, algebraic. --- Global differential geometry. --- Differential equations, partial. --- Partial differential equations --- Geometry, Differential --- Number study --- Numbers, Theory of --- Algebra --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Differential geometry --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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Anàlisi harmònica --- Grups de Lie --- Geometria algebraica --- Grups topològics --- Grups continus --- Topologia --- H-espais --- Grups compactes --- Grups localment compactes --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes --- Espais simètrics --- Espais homogenis --- Grups de Lie semisimples --- Àlgebres de Banach --- Càlcul --- Àlgebres de mesura --- Harmòniques esfèriques --- Ondetes (Matemàtica) --- Anàlisi de Fourier --- Anàlisi de sèries temporals --- Funcions de Bessel --- Harmonic analysis --- Lie groups --- Geometry, Algebraic

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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.

Group theory --- Algebraic geometry --- Differential geometry. Global analysis --- Geometry --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Fourieranalyse --- analyse (wiskunde) --- topologie (wiskunde) --- Fourierreeksen --- mathematische modellen --- statistiek --- wiskunde --- geometrie

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Group theory --- Algebraic geometry --- Differential geometry. Global analysis --- Geometry --- Harmonic analysis. Fourier analysis --- Mathematical analysis --- Mathematics --- Fourieranalyse --- analyse (wiskunde) --- topologie (wiskunde) --- Fourierreeksen --- mathematische modellen --- statistiek --- wiskunde --- geometrie