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This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing.Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Algebraic geometry --- Differential geometry. Global analysis --- Link theory. --- Curves, Plane. --- SINGULARITIES (Mathematics) --- Curves, Plane --- Invariants --- Link theory --- Singularities (Mathematics) --- Geometry, Algebraic --- Low-dimensional topology --- Piecewise linear topology --- Higher plane curves --- Plane curves --- Invariants. --- 3-sphere. --- Alexander Grothendieck. --- Alexander polynomial. --- Algebraic curve. --- Algebraic equation. --- Algebraic geometry. --- Algebraic surface. --- Algorithm. --- Ambient space. --- Analytic function. --- Approximation. --- Big O notation. --- Call graph. --- Cartesian coordinate system. --- Characteristic polynomial. --- Closed-form expression. --- Cohomology. --- Computation. --- Conjecture. --- Connected sum. --- Contradiction. --- Coprime integers. --- Corollary. --- Curve. --- Cyclic group. --- Determinant. --- Diagram (category theory). --- Diffeomorphism. --- Dimension. --- Disjoint union. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Euler number. --- Existential quantification. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Foliation. --- Fundamental group. --- Geometry. --- Graph (discrete mathematics). --- Ground field. --- Homeomorphism. --- Homology sphere. --- Identity matrix. --- Integer matrix. --- Intersection form (4-manifold). --- Isolated point. --- Isolated singularity. --- Jordan normal form. --- Knot theory. --- Mathematical induction. --- Monodromy matrix. --- Monodromy. --- N-sphere. --- Natural transformation. --- Newton polygon. --- Newton's method. --- Normal (geometry). --- Notation. --- Pairwise. --- Parametrization. --- Plane curve. --- Polynomial. --- Power series. --- Projective plane. --- Puiseux series. --- Quantity. --- Rational function. --- Resolution of singularities. --- Riemann sphere. --- Riemann surface. --- Root of unity. --- Scientific notation. --- Seifert surface. --- Set (mathematics). --- Sign (mathematics). --- Solid torus. --- Special case. --- Stereographic projection. --- Submanifold. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Torus knot. --- Torus. --- Tubular neighborhood. --- Unit circle. --- Unit vector. --- Unknot. --- Variable (mathematics).

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This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.

Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analyse harmonique --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groupe de Heisenberg. --- Addition. --- Analytic function. --- Asymptote. --- Asymptotic analysis. --- Asymptotic expansion. --- Asymptotic formula. --- Automorphism. --- Axiom. --- Banach space. --- Bessel function. --- Big O notation. --- Bilinear form. --- Borel measure. --- Boundary value problem. --- Bounded function. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cancellation property. --- Cauchy's integral theorem. --- Cauchy–Riemann equations. --- Characteristic polynomial. --- Characterization (mathematics). --- Commutative property. --- Commutator. --- Complex analysis. --- Convolution. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Dirac delta function. --- Dirichlet problem. --- Elliptic operator. --- Existential quantification. --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hölder's inequality. --- Infimum and supremum. --- Integral transform. --- Interpolation theorem. --- Lagrangian (field theory). --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Locally integrable function. --- Marcinkiewicz interpolation theorem. --- Martingale (probability theory). --- Mathematical induction. --- Maximal function. --- Meromorphic function. --- Multiplication operator. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Number theory. --- Operator theory. --- Order of integration (calculus). --- Orthogonality. --- Oscillatory integral. --- Poisson summation formula. --- Projection (linear algebra). --- Pseudo-differential operator. --- Pseudoconvexity. --- Rectangle. --- Riesz transform. --- Several complex variables. --- Sign (mathematics). --- Singular integral. --- Sobolev space. --- Special case. --- Spectral theory. --- Square (algebra). --- Stochastic differential equation. --- Subharmonic function. --- Submanifold. --- Summation. --- Support (mathematics). --- Theorem. --- Translational symmetry. --- Uniqueness theorem. --- Variable (mathematics). --- Vector field. --- Fourier, Analyse de --- Fourier, Opérateurs intégraux de

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This book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.

512 --- Characters of groups --- Finite fields (Algebra) --- Finite groups --- Groups, Finite --- Group theory --- Modules (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Characters, Group --- Group characters --- Groups, Characters of --- Representations of groups --- Rings (Algebra) --- Algebra --- 512 Algebra --- Finite groups. --- Characters of groups. --- Addition. --- Algebra representation. --- Algebraic closure. --- Algebraic group. --- Algebraic variety. --- Algebraically closed field. --- Bijection. --- Borel subgroup. --- Cartan subalgebra. --- Character table. --- Character theory. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Class function (algebra). --- Classical group. --- Coefficient. --- Cohomology with compact support. --- Cohomology. --- Combination. --- Complex number. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Coxeter group. --- Cyclic group. --- Cyclotomic polynomial. --- David Kazhdan. --- Dense set. --- Derived category. --- Diagram (category theory). --- Dimension. --- Direct sum. --- Disjoint sets. --- Disjoint union. --- E6 (mathematics). --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Equivalence relation. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fiber bundle. --- Finite field. --- Finite group. --- Fourier transform. --- Green's function. --- Group (mathematics). --- Group action. --- Group representation. --- Harish-Chandra. --- Hecke algebra. --- Identity element. --- Integer. --- Irreducible representation. --- Isomorphism class. --- Jordan decomposition. --- Line bundle. --- Linear combination. --- Local system. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monodromy. --- Morphism. --- Orthonormal basis. --- P-adic number. --- Parametrization. --- Parity (mathematics). --- Partially ordered set. --- Perverse sheaf. --- Pointwise. --- Polynomial. --- Quantity. --- Rational point. --- Reductive group. --- Ree group. --- Schubert variety. --- Scientific notation. --- Semisimple Lie algebra. --- Sheaf (mathematics). --- Simple group. --- Simple module. --- Special case. --- Standard basis. --- Subset. --- Subtraction. --- Summation. --- Surjective function. --- Symmetric group. --- Tensor product. --- Theorem. --- Two-dimensional space. --- Unipotent representation. --- Vector bundle. --- Vector space. --- Verma module. --- Weil conjecture. --- Weyl group. --- Zariski topology.

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In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cramér's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow. For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance.

Mathematical statistics --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistique mathématique --- Mathematical statistics. --- Statistique mathématique --- Statistique mathématique. --- Distribution (théorie des probabilités) --- Distribution (Probability theory) --- A priori probability. --- Addition theorem. --- Additive function. --- Analysis of covariance. --- Arithmetic mean. --- Axiom. --- Bayes' theorem. --- Bias of an estimator. --- Binomial distribution. --- Binomial theorem. --- Bolzano–Weierstrass theorem. --- Borel set. --- Bounded set (topological vector space). --- Calculation. --- Cartesian product. --- Central moment. --- Characteristic function (probability theory). --- Characteristic polynomial. --- Coefficient. --- Commutative property. --- Confidence interval. --- Convergence of random variables. --- Correlation coefficient. --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Diagram (category theory). --- Dimension. --- Distribution (mathematics). --- Distribution function. --- Empirical distribution function. --- Equation. --- Estimation theory. --- Estimation. --- Identity matrix. --- Independence (probability theory). --- Interval (mathematics). --- Inverse probability. --- Invertible matrix. --- Joint probability distribution. --- Laplace distribution. --- Lebesgue integration. --- Lebesgue measure. --- Lebesgue–Stieltjes integration. --- Likelihood function. --- Limit (mathematics). --- Linear regression. --- Logarithm. --- Logarithmic derivative. --- Logarithmic scale. --- Marginal distribution. --- Mathematical analysis. --- Mathematical induction. --- Mathematical theory. --- Mathematics. --- Matrix (mathematics). --- Maxima and minima. --- Measure (mathematics). --- Method of moments (statistics). --- Metric space. --- Minor (linear algebra). --- Moment (mathematics). --- Moment matrix. --- Normal distribution. --- Numerical analysis. --- Parameter. --- Parity (mathematics). --- Poisson distribution. --- Probability distribution. --- Probability theory. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Random variable. --- Realization (probability). --- Riemann integral. --- Sample space. --- Sampling (statistics). --- Scientific notation. --- Series (mathematics). --- Set (mathematics). --- Set function. --- Sign (mathematics). --- Standard deviation. --- Statistic. --- Statistical Science. --- Statistical hypothesis testing. --- Statistical inference. --- Statistical regularity. --- Statistical theory. --- Subset. --- Summation. --- Theorem. --- Theory. --- Transfinite number. --- Uniform distribution (discrete). --- Variable (mathematics). --- Variance. --- Weighted arithmetic mean. --- Z-test. --- Distribution (théorie des probabilités)

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This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.

Continuous groups. --- Additive group. --- Adjoint representation. --- Algebra over a field. --- Algebraic extension. --- Algebraic variety. --- Algebraically closed field. --- Analytic function. --- Analytic manifold. --- Automorphism. --- Axiom of countability. --- Ball (mathematics). --- Cardinal number. --- Characteristic polynomial. --- Coefficient. --- Commutator subgroup. --- Complex number. --- Connected component (graph theory). --- Continuous function (set theory). --- Continuous function. --- Coordinate system. --- Coset. --- Countable set. --- Covering group. --- Covering space. --- Differential algebra. --- Differential calculus. --- Differential form. --- Differential of a function. --- Dual space. --- Eigenvalues and eigenvectors. --- Endomorphism. --- Equivalence class. --- Existential quantification. --- Exponential function. --- Exterior algebra. --- Fundamental group. --- Galois group. --- General topology. --- Geometry. --- Group (mathematics). --- Group theory. --- Hermitian matrix. --- Homeomorphism. --- Homogeneous space. --- Homomorphism. --- Homotopy group. --- Identity element. --- Identity matrix. --- Infinitesimal transformation. --- Integer. --- Invariant subspace. --- Irreducible representation. --- Kronecker product. --- Lie algebra. --- Lie group. --- Linear function. --- Linear map. --- Linear space (geometry). --- Linear subspace. --- Linearization. --- Locally connected space. --- Manifold. --- Mathematical induction. --- Matrix exponential. --- Modular arithmetic. --- Module (mathematics). --- Monodromy. --- Morphism. --- Open set. --- Orthogonal group. --- Parametric equation. --- Permutation. --- Power series. --- Projective plane. --- Real number. --- Regular matrix. --- Representation theory. --- Riemann surface. --- Simply connected space. --- Skew-symmetric matrix. --- Special case. --- Subalgebra. --- Subgroup. --- Submanifold. --- Subset. --- Summation. --- Symplectic geometry. --- Symplectic group. --- Tangent space. --- Theorem. --- Topological group. --- Topological space. --- Topology. --- Trigonometric polynomial. --- Union (set theory). --- Uniqueness theorem. --- Unitary group. --- Unitary matrix. --- Variable (mathematics). --- Vector space.