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Random Fourier series with applications to harmonic analysis.
Authors: ---
ISBN: 0691082898 0691082928 1400881536 Year: 1981 Volume: no. 101 Publisher: Princeton (N.J.) : Princeton university press,

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Abstract

In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.The major results depend heavily on the Dudley-Fernique necessary and sufficient condition for the continuity of stationary Gaussian processes and on recent work on sums of independent Banach space valued random variables. It is noteworthy that the proofs for the Abelian case immediately extend to the non-Abelian case once the proper definition of random Fourier series is made. In doing this the authors obtain new results on sums of independent random matrices with elements in a Banach space. The final chapter of the book suggests several directions for further research.

Keywords

Harmonic analysis. Fourier analysis --- Fourier series. --- Harmonic analysis. --- Fourier, Séries de --- Analyse harmonique --- 517.518.4 --- Fourier series --- Harmonic analysis --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Harmonic functions --- Time-series analysis --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Fourier analysis --- 517.518.4 Trigonometric series --- Fourier, Séries de --- Abelian group. --- Almost periodic function. --- Almost surely. --- Banach space. --- Big O notation. --- Cardinality. --- Central limit theorem. --- Circle group. --- Coefficient. --- Commutative property. --- Compact group. --- Compact space. --- Complex number. --- Continuous function. --- Corollary. --- Discrete group. --- Equivalence class. --- Existential quantification. --- Finite group. --- Gaussian process. --- Haar measure. --- Independence (probability theory). --- Inequality (mathematics). --- Integer. --- Irreducible representation. --- Non-abelian group. --- Non-abelian. --- Normal distribution. --- Orthogonal group. --- Orthogonal matrix. --- Probability distribution. --- Probability measure. --- Probability space. --- Probability. --- Random function. --- Random matrix. --- Random variable. --- Rate of convergence. --- Real number. --- Ring (mathematics). --- Scientific notation. --- Set (mathematics). --- Slepian's lemma. --- Small number. --- Smoothness. --- Stationary process. --- Subgroup. --- Subset. --- Summation. --- Theorem. --- Uniform convergence. --- Unitary matrix. --- Variance.

Riemann surfaces and related topics: proceedings of the 1978 Stony Brook Conference
Authors: ---
ISBN: 0691082642 0691082677 1400881552 Year: 1981 Publisher: Princeton, N.J.

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Abstract

The description for this book, Riemann Surfaces Related Topics (AM-97), Volume 97: Proceedings of the 1978 Stony Brook Conference. (AM-97), will be forthcoming.

Keywords

Geometry --- Riemann surfaces --- -517.54 --- Surfaces, Riemann --- Functions --- Congresses --- Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- 517.54 Conformal mapping and geometric problems in the theory of functions of a complex variable. Analytic functions and their generalizations --- 517.54 --- Riemann, Surfaces de --- Abstract simplicial complex. --- Affine transformation. --- Algebraic curve. --- Algebraic element. --- Algebraic equation. --- Algebraic surface. --- Analytic function. --- Analytic torsion. --- Automorphic form. --- Automorphic function. --- Automorphism. --- Banach space. --- Basis (linear algebra). --- Boundary (topology). --- Bounded set (topological vector space). --- Cohomology ring. --- Cohomology. --- Commutative property. --- Commutator subgroup. --- Compact Riemann surface. --- Complex analysis. --- Complex manifold. --- Conformal geometry. --- Conformal map. --- Conjugacy class. --- Covering space. --- Diagram (category theory). --- Dimension (vector space). --- Divisor (algebraic geometry). --- Divisor. --- Eigenvalues and eigenvectors. --- Equivalence class. --- Equivalence relation. --- Ergodic theory. --- Existential quantification. --- Foliation. --- Fuchsian group. --- Fundamental domain. --- Fundamental group. --- Fundamental polygon. --- Geodesic. --- Geometric function theory. --- Group homomorphism. --- H-cobordism. --- Hausdorff measure. --- Holomorphic function. --- Homeomorphism. --- Homomorphism. --- Homotopy. --- Hyperbolic 3-manifold. --- Hyperbolic manifold. --- Hyperbolic space. --- Infimum and supremum. --- Injective module. --- Interior (topology). --- Intersection form (4-manifold). --- Isometry. --- Isomorphism class. --- Jordan curve theorem. --- Kleinian group. --- Kähler manifold. --- Limit point. --- Limit set. --- Manifold. --- Meromorphic function. --- Metric space. --- Mostow rigidity theorem. --- Möbius transformation. --- Poincaré conjecture. --- Pole (complex analysis). --- Polynomial. --- Product topology. --- Projective variety. --- Quadratic differential. --- Quasi-isometry. --- Quasiconformal mapping. --- Quotient space (topology). --- Radon–Nikodym theorem. --- Ricci curvature. --- Riemann mapping theorem. --- Riemann sphere. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Schwarzian derivative. --- Strictly convex space. --- Subgroup. --- Submanifold. --- Surjective function. --- Tangent space. --- Teichmüller space. --- Theorem. --- Topological conjugacy. --- Topological space. --- Topology. --- Uniformization theorem. --- Uniformization. --- Uniqueness theorem. --- Unit disk. --- Vector bundle.

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