TY - BOOK ID - 8581626 TI - Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group AU - Volchkov, Valery V. AU - Volchkov, Vitaly V. PY - 2009 SN - 1447122836 1848825323 9786612333194 1282333194 1848825331 PB - London : Springer London : Imprint: Springer, DB - UniCat KW - Harmonic analysis. KW - Lie groups. KW - Nilpotent Lie groups. KW - Periodic functions. KW - Symmetric spaces. KW - Harmonic analysis KW - Symmetric spaces KW - Nilpotent Lie groups KW - Operations Research KW - Civil & Environmental Engineering KW - Engineering & Applied Sciences KW - Spectral synthesis (Mathematics) KW - Synthesis, Spectral (Mathematics) KW - Analysis (Mathematics) KW - Functions, Potential KW - Potential functions KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Approximation theory. KW - Fourier analysis. KW - Functional analysis. KW - Integral equations. KW - Special functions. KW - Analysis. KW - Functional Analysis. KW - Fourier Analysis. KW - Integral Equations. KW - Special Functions. KW - Approximations and Expansions. KW - Special functions KW - Mathematical analysis KW - Equations, Integral KW - Functional equations KW - Functional analysis KW - Functional calculus KW - Calculus of variations KW - Integral equations KW - Analysis, Fourier KW - Theory of approximation KW - Functions KW - Polynomials KW - Chebyshev systems KW - 517.1 Mathematical analysis KW - Math KW - Science KW - Group theory KW - Spectral theory (Mathematics) KW - Banach algebras KW - Calculus KW - Mathematics KW - Bessel functions KW - Fourier series KW - Harmonic functions KW - Time-series analysis KW - Global analysis (Mathematics). KW - Functions, special. KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic UR - https://www.unicat.be/uniCat?func=search&query=sysid:8581626 AB - This 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. Highly topical, 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 have included an introductory section that develops analysis on symmetric spaces without the 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. ER -