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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.
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.
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 on
December 2013. The last seminar, which took place 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.
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 on
December 2013. The last seminar, which took place 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.
This book includes selected papers presented at the MIMS
(Mediterranean Institute for the Mathematical Sciences) - GGTM
(Geometry and Topology Grouping for the Maghreb) conference, held
in memory of Mohammed Salah Baouendi, a most renowned figure in the
field of several complex variables, who passed away in 2011. All
research articles were written by leading experts, some of whom are
prize winners in the fields of complex geometry, algebraic geometry
and analysis. The book offers a valuable resource for all
researchers interested in recent developments in analysis and
geometry.
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.
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.
This book includes selected papers presented at the MIMS
(Mediterranean Institute for the Mathematical Sciences) - GGTM
(Geometry and Topology Grouping for the Maghreb) conference, held
in memory of Mohammed Salah Baouendi, a most renowned figure in the
field of several complex variables, who passed away in 2011. All
research articles were written by leading experts, some of whom are
prize winners in the fields of complex geometry, algebraic geometry
and analysis. The book offers a valuable resource for all
researchers interested in recent developments in analysis and
geometry.
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