|
Showing 1 - 4 of
4 matches in All Departments
The book demonstrates the development of integral geometry on
domains of homogeneous spaces since 1990. It covers a wide range of
topics, including analysis on multidimensional Euclidean domains
and Riemannian symmetric spaces of arbitrary ranks as well as
recent work on phase space and the Heisenberg group. The book
includes many significant recent results, some of them hitherto
unpublished, among which can be pointed out uniqueness theorems for
various classes of functions, far-reaching generalizations of the
two-radii problem, the modern versions of the Pompeiu problem, and
explicit reconstruction formulae in problems of integral geometry.
These results are intriguing and useful in various fields of
contemporary mathematics. The proofs given are "minimal" in the
sense that they involve only those concepts and facts which are
indispensable for the essence of the subject. Each chapter provides
a historical perspective on the results presented and includes many
interesting open problems. Readers will find this book relevant to
harmonic analysis on homogeneous spaces, invariant spaces theory,
integral transforms on symmetric spaces and the Heisenberg group,
integral equations, special functions, and transmutation operators
theory.
The book demonstrates the development of integral geometry on
domains of homogeneous spaces since 1990. It covers a wide range of
topics, including analysis on multidimensional Euclidean domains
and Riemannian symmetric spaces of arbitrary ranks as well as
recent work on phase space and the Heisenberg group. The book
includes many significant recent results, some of them hitherto
unpublished, among which can be pointed out uniqueness theorems for
various classes of functions, far-reaching generalizations of the
two-radii problem, the modern versions of the Pompeiu problem, and
explicit reconstruction formulae in problems of integral geometry.
These results are intriguing and useful in various fields of
contemporary mathematics. The proofs given are "minimal" in the
sense that they involve only those concepts and facts which are
indispensable for the essence of the subject. Each chapter provides
a historical perspective on the results presented and includes many
interesting open problems. Readers will find this book relevant to
harmonic analysis on homogeneous spaces, invariant spaces theory,
integral transforms on symmetric spaces and the Heisenberg group,
integral equations, special functions, and transmutation operators
theory.
The theory of mean periodic functions is a subject which goes back
to works of Littlewood, Delsarte, John and that has undergone a
vigorous development in recent years. There has been much progress
in a number of problems concerning local - pects of spectral
analysis and spectral synthesis on homogeneous spaces. The study
oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic
analysis, complex analysis, partial differential equations,
integral geometry, appr- imation theory, and other branches of
contemporary mathematics. The present book describes recent
advances in this direction of research. Symmetric spaces and the
Heisenberg group are an active ?eld of investigation at 2 the
moment. The simplest examples of symmetric spaces, the classical
2-sphere S 2 and the hyperbolic plane H , play familiar roles in
many areas in mathematics. The n Heisenberg groupH is a principal
model for nilpotent groups, and results obtained n forH may suggest
results that hold more generally for this important class of Lie
groups. The purpose of this book is to develop harmonic analysis of
mean periodic functions on the above spaces.
The theory of mean periodic functions is a subject which goes back
to works of Littlewood, Delsarte, John and that has undergone a
vigorous development in recent years. There has been much progress
in a number of problems concerning local - pects of spectral
analysis and spectral synthesis on homogeneous spaces. The study
oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic
analysis, complex analysis, partial differential equations,
integral geometry, appr- imation theory, and other branches of
contemporary mathematics. The present book describes recent
advances in this direction of research. Symmetric spaces and the
Heisenberg group are an active ?eld of investigation at 2 the
moment. The simplest examples of symmetric spaces, the classical
2-sphere S 2 and the hyperbolic plane H , play familiar roles in
many areas in mathematics. The n Heisenberg groupH is a principal
model for nilpotent groups, and results obtained n forH may suggest
results that hold more generally for this important class of Lie
groups. The purpose of this book is to develop harmonic analysis of
mean periodic functions on the above spaces.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|