Overview
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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
Full Product Details
Author: Valery V. Volchkov ,
Vitaly V. Volchkov
Publisher: Birkhauser Verlag AG
Imprint: Birkhauser Verlag AG
Edition: 2013 ed.
Dimensions:
Width: 15.50cm
, Height: 3.10cm
, Length: 23.50cm
Weight: 9.007kg
ISBN: 9783034808002
ISBN 10: 3034808003
Pages: 592
Publication Date: 26 June 2015
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
From the reviews: The book presents a broad survey of the results in an interesting area, where the harmonic analysis and differential and integral equations interact in a fruitful way. The authors themselves have contributed a lot to the subject. The book will be interesting to those working in the border areas between analysis, integral geometry and Lie groups representation theory. (Mark Agranovsky, Mathematical Reviews, March, 2014)
From the reviews: The book presents a broad survey of the results in an interesting area, where the harmonic analysis and differential and integral equations interact in a fruitful way. The authors themselves have contributed a lot to the subject. The book will be interesting to those working in the border areas between analysis, integral geometry and Lie groups representation theory. (Mark Agranovsky, Mathematical Reviews, March, 2014)
From the reviews: “The book presents a broad survey of the results in an interesting area, where the harmonic analysis and differential and integral equations interact in a fruitful way. The authors themselves have contributed a lot to the subject. The book will be interesting to those working in the border areas between analysis, integral geometry and Lie groups representation theory.” (Mark Agranovsky, Mathematical Reviews, March, 2014)
From the reviews: The book presents a broad survey of the results in an interesting area, where the harmonic analysis and differential and integral equations interact in a fruitful way. The authors themselves have contributed a lot to the subject. The book will be interesting to those working in the border areas between analysis, integral geometry and Lie groups representation theory. (Mark Agranovsky, Mathematical Reviews, March, 2014)
