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This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.
Convex sets. --- Fourier series. --- Spherical harmonics. --- Functions, Potential --- Potential functions --- Harmonic analysis --- Harmonic functions --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Sets, Convex --- Convex domains --- Set theory
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This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.
Series, Infinite --- Analytic functions --- Harmonic analysis --- 515.243 --- Infinite series --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Mathematical Sciences --- General and Others --- Series, Infinite. --- Functions. --- Harmonic analysis. --- Differential equations --- Numbers, Complex --- Set theory --- Analytic functions. --- Functions
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Mathematical control systems --- Numerical analysis --- Computer. Automation --- Harmonic analysis. Fourier analysis --- Mathematics --- Ergodic theory. Information theory --- Discrete mathematics --- Engineering mathematics --- Electrical engineering --- Electronics --- 51-7 --- Electric engineering --- -Electronics --- -Engineering mathematics --- #WWIS:AGGR --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical sciences --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Engineering mathematics. --- Mathematics. --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathématiques de l'ingénieur --- Mathématiques --- Electrical engineering - Mathematics --- Electronics - Mathematics
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Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Differential dynamical systems --- Drie-menigvuldigheden (Topologie) --- Three-manifolds (Topology) --- Trois-variétés (Topologie) --- Differentiable dynamical systems. --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Low-dimensional topology --- Topological manifolds --- Algebraic topology. --- Analytic continuation. --- Automorphism. --- Beltrami equation. --- Bifurcation theory. --- Boundary (topology). --- Cantor set. --- Circular symmetry. --- Combinatorics. --- Compact space. --- Complex conjugate. --- Complex manifold. --- Complex number. --- Complex plane. --- Conformal geometry. --- Conformal map. --- Conjugacy class. --- Convex hull. --- Covering space. --- Deformation theory. --- Degeneracy (mathematics). --- Dimension (vector space). --- Disk (mathematics). --- Dynamical system. --- Eigenvalues and eigenvectors. --- Factorization. --- Fiber bundle. --- Fuchsian group. --- Fundamental domain. --- Fundamental group. --- Fundamental solution. --- G-module. --- Geodesic. --- Geometry. --- Harmonic analysis. --- Hausdorff dimension. --- Homeomorphism. --- Homotopy. --- Hyperbolic 3-manifold. --- Hyperbolic geometry. --- Hyperbolic manifold. --- Hyperbolic space. --- Hypersurface. --- Infimum and supremum. --- Injective function. --- Intersection (set theory). --- Invariant subspace. --- Isometry. --- Julia set. --- Kleinian group. --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Limit point. --- Limit set. --- Linear map. --- Mandelbrot set. --- Manifold. --- Mapping class group. --- Measure (mathematics). --- Moduli (physics). --- Moduli space. --- Modulus of continuity. --- Möbius transformation. --- N-sphere. --- Newton's method. --- Permutation. --- Point at infinity. --- Polynomial. --- Quadratic function. --- Quasi-isometry. --- Quasiconformal mapping. --- Quasisymmetric function. --- Quotient space (topology). --- Radon–Nikodym theorem. --- Renormalization. --- Representation of a Lie group. --- Representation theory. --- Riemann sphere. --- Riemann surface. --- Riemannian manifold. --- Schwarz lemma. --- Simply connected space. --- Special case. --- Submanifold. --- Subsequence. --- Support (mathematics). --- Tangent space. --- Teichmüller space. --- Theorem. --- Topology of uniform convergence. --- Topology. --- Trace (linear algebra). --- Transversal (geometry). --- Transversality (mathematics). --- Triangle inequality. --- Unit disk. --- Unit sphere. --- Upper and lower bounds. --- Vector field. --- Differentiable dynamical systems --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds
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