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Spectral synthesis

Functional analysis --- Differential equations --- Locally compact Abelian groups --- Spectral synthesis (Mathematics) --- Tauberian theorems --- #KVIV --- #WWIS:STAT --- 517.518.1 --- 517.518.1 Measure. Integration. Differentiation --- Measure. Integration. Differentiation --- Series, Infinite --- Synthesis, Spectral (Mathematics) --- Group theory --- Harmonic analysis --- Spectral theory (Mathematics) --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Spectral synthesis (Mathematics). --- Locally compact Abelian groups. --- Tauberian theorems. --- 517.5 --- Banach, Algèbres de --- Fourier, Analyse de --- Banach, Algèbres de --- Théorèmes taubériens --- 517.5 Theory of functions --- Theory of functions

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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.

Harmonic analysis. --- Lie groups. --- Nilpotent Lie groups. --- Periodic functions. --- Symmetric spaces. --- Harmonic analysis --- Symmetric spaces --- Nilpotent Lie groups --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Spectral synthesis (Mathematics) --- Synthesis, Spectral (Mathematics) --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Approximation theory. --- Fourier analysis. --- Functional analysis. --- Integral equations. --- Special functions. --- Analysis. --- Functional Analysis. --- Fourier Analysis. --- Integral Equations. --- Special Functions. --- Approximations and Expansions. --- Special functions --- Mathematical analysis --- Equations, Integral --- Functional equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Integral equations --- Analysis, Fourier --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- 517.1 Mathematical analysis --- Math --- Science --- Group theory --- Spectral theory (Mathematics) --- Banach algebras --- Calculus --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Global analysis (Mathematics). --- Functions, special. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic