Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
The book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces.
The main purpose of this book is the study of local aspects of spectral analysis and spectral synthesis on Euclidean spaces, Riemannian symmetric spaces of an arbitrary rank and Heisenberg groups. The subject can be viewed as arising from three classical topics: John’s support theorem, Schwartz’s fundamental principle, and Delsarte’s two-radii theorem.
Very up-to-date, the book contains most of the significant recent results in this area with complete and detailed proofs. In order to make this book accessible to a wide audience, the authors provide an introductory part developing analysis on symmetric spaces without use of Lie theory. Challenging open problems are described and explained, and promising new research directions are indicated.
Designed for both experts and beginners in the field, the book is rich in methods for a wide variety of problems in many areas of mathematics.
The approach employed in this book is the best suited for dealing with the subject in a systematic fashion.
Most of the results are the best possible, giving answers to all questions that naturally arise in the topic and presenting the complete picture of corresponding phenomenon
Some significant results are published here for the first time
The proofs only involve concepts and facts which are indispensable to the essence of the subject
There is no other book available that features the same treatment of symmetric spaces