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Graduate students in the natural sciences-including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy-need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike an online illustration package is available to professors

Geophysics --- Cosmic physics --- Physics --- Space sciences --- Mathematics. --- Analytical mechanics. --- Applied mathematics. --- Atmospheric physics. --- Bessel function. --- Bifurcation theory. --- Calculation. --- Calculus of variations. --- Cartesian coordinate system. --- Cauchy's theorem (geometry). --- Celestial mechanics. --- Central limit theorem. --- Chaos theory. --- Classical electromagnetism. --- Classical mechanics. --- Classical physics. --- Convolution theorem. --- Deformation (mechanics). --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential equation. --- Drag (physics). --- Earth science. --- Eigenvalues and eigenvectors. --- Einstein notation. --- Elliptic integral. --- Elliptic orbit. --- Equation. --- Expectation value (quantum mechanics). --- Figure of the Earth. --- Forcing function (differential equations). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Function (mathematics). --- Gaussian function. --- Geochemistry. --- Geochronology. --- Geodesics in general relativity. --- Geometry. --- Geophysics. --- Gravitational acceleration. --- Gravitational constant. --- Gravitational potential. --- Gravitational two-body problem. --- Hamiltonian mechanics. --- Handbook of mathematical functions. --- Harmonic oscillator. --- Helmholtz equation. --- Hilbert transform. --- Hyperbolic partial differential equation. --- Integral equation. --- Isotope geochemistry. --- Lagrangian (field theory). --- Laplace transform. --- Laplace's equation. --- Laws of thermodynamics. --- Limit (mathematics). --- Line (geometry). --- Lorenz system. --- Mathematical analysis. --- Mathematical geophysics. --- Mathematical physics. --- Newton's law of universal gravitation. --- Newton's laws of motion. --- Newton's method. --- Newtonian dynamics. --- Numerical analysis. --- Numerical integration. --- Operator (physics). --- Orbit. --- Orbital resonance. --- Parseval's theorem. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Planetary body. --- Planetary science. --- Poisson's equation. --- Pole (complex analysis). --- Proportionality (mathematics). --- Quantum mechanics. --- Rotation (mathematics). --- Satellite geodesy. --- Scalar (physics). --- Scientific notation. --- Separatrix (mathematics). --- Sign (mathematics). --- Space physics. --- Statistical mechanics. --- Stokes' theorem. --- Three-dimensional space (mathematics). --- Transformation geometry. --- Trapezoidal rule. --- Truncation error (numerical integration). --- Two-dimensional space. --- Van der Pol oscillator. --- Variable (mathematics). --- Vector space. --- Wave equation.

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This work deals with an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups. In this general setting there are applications to a variety of problems, such as those arising in the study of the expansions coming from second order elliptic operators. A review of background material in Lie groups and martingale theory is included to make the monograph more accessible to the student.

Harmonic analysis. Fourier analysis --- Harmonic analysis --- Semigroups --- 517.986.6 --- Lie groups --- Littlewood-Paley theory --- #WWIS:d.d. Prof. L. Bouckaert/BOUC --- Fourier analysis --- Functions of several real variables --- Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Harmonic analysis of functions of groups and homogeneous spaces --- Harmonic analysis. --- Littlewood-Paley theory. --- Lie groups. --- Semigroups. --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- Addition. --- Analytic function. --- Axiom. --- Boundary value problem. --- Central limit theorem. --- Change of variables. --- Circle group. --- Classification theorem. --- Commutative property. --- Compact group. --- Complex analysis. --- Convex set. --- Coset. --- Covering space. --- Derivative. --- Differentiable manifold. --- Differential geometry. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Direct sum. --- E6 (mathematics). --- E7 (mathematics). --- E8 (mathematics). --- Elementary proof. --- Equation. --- Equivalence class. --- Existence theorem. --- Existential quantification. --- Fourier analysis. --- Fourier series. --- Fourier transform. --- Function space. --- General linear group. --- Haar measure. --- Harmonic function. --- Hermite polynomials. --- Hilbert transform. --- Homogeneous space. --- Homomorphism. --- Ideal (ring theory). --- Identity matrix. --- Indecomposability. --- Integral transform. --- Invariant measure. --- Invariant subspace. --- Irreducibility (mathematics). --- Irreducible representation. --- Lebesgue measure. --- Legendre polynomials. --- Lie algebra. --- Lie group. --- Linear combination. --- Linear map. --- Local diffeomorphism. --- Markov process. --- Martingale (probability theory). --- Matrix group. --- Measurable function. --- Measure (mathematics). --- Multiple integral. --- Normal subgroup. --- One-dimensional space. --- Open set. --- Ordinary differential equation. --- Orthogonality. --- Orthonormality. --- Parseval's theorem. --- Partial differential equation. --- Probability space. --- Quadratic form. --- Rank of a group. --- Regular representation. --- Riemannian manifold. --- Riesz transform. --- Schur orthogonality relations. --- Scientific notation. --- Semigroup. --- Sequence. --- Special case. --- Stone–Weierstrass theorem. --- Sturm–Liouville theory. --- Subgroup. --- Subset. --- Summation. --- Tensor algebra. --- Tensor product. --- Theorem. --- Theory. --- Topological group. --- Topological space. --- Torus. --- Trigonometric polynomial. --- Trivial representation. --- Uniform convergence. --- Unitary operator. --- Unitary representation. --- Vector field. --- Vector space. --- Lie, Groupes de --- Analyse harmonique