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In this book, a distinguished expert introduces plasma physics from the ground up, presenting it as a comprehensible field that can be grasped largely on the basis of physical intuition and qualitative reasoning, similar to other fields of physics. Plasmas are ionized gases that can be found in a hydrogen bomb explosion, the confinement chamber of an experimental fusion reactor, the solar corona, the aurora borealis, the interstellar medium, and the immediate vicinity of a gravitational black hole. Not surprisingly, plasma physics appears to consist of numerous topics arising independently from astrophysics, fusion physics, and other practical applications, and hence it remains a field poorly understood even by many astrophysicists. But, in fact, most of these topics can be approached from the same perspective, with a simple, physical intuition. Selecting simple examples and presenting them in a simultaneously intuitive and rigorous manner, Russell Kulsrud guides readers through a careful derivation of the results and allows them to think through the physics for themselves. Thus, they are better prepared for complex cases and more general results. The first eleven chapters present topics by their importance to plasma physics while the last three chapters emphasize the field's astrophysical applications, applying the results accrued earlier. Throughout, many problems illustrate the field's applications. Based on a course the author taught for many years, Plasma Physics for Astrophysics is intended for graduate students as well as for working astrophysicists.

Plasma astrophysics. --- Accretion disk. --- Alfven time. --- Bessel function. --- Braginski equations. --- Charge neutrality. --- Compression. --- Contour integration. --- Critical drift velocity. --- Dalembertian solution. --- Debye length. --- Downstream region. --- Earth's magnetic field. --- Entropy. --- Faraday rotation. --- Flux freezing. --- Guide field. --- Helicity spectrum. --- Impact parameter. --- Ion acoustic mode. --- Jump conditions. --- Laplace transform. --- Magnetic reconnection. --- Magnetic tension. --- Maxwell distribution. --- Ohm's law. --- Parallel viscosity. --- Quasi neutrality. --- Shocks. --- Solar flare. --- Topology.

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The description for this book, An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18, will be forthcoming.

Functional equations. --- Addition. --- Antiderivative. --- Asymptotic formula. --- Bessel function. --- Beta function. --- Boundary value problem. --- Change of variables. --- Closed-form expression. --- Coefficient. --- Combination. --- Continuous function. --- Corollary. --- Differential equation. --- Enumeration. --- Equation. --- Existential quantification. --- Explicit formula. --- Exponential function. --- Factorial. --- Function (mathematics). --- Functional equation. --- Hermite polynomials. --- Hypergeometric function. --- Integer. --- Laguerre polynomials. --- Laplace transform. --- Legendre function. --- Linear difference equation. --- Linear differential equation. --- Mathematical induction. --- Mathematician. --- Monomial. --- Natural number. --- Number theory. --- Ordinary differential equation. --- Parameter. --- Periodic function. --- Polygamma function. --- Polynomial. --- Potential theory. --- Power series. --- Rectangle. --- Recurrence relation. --- Remainder. --- Scientific notation. --- Sequent. --- Simple function. --- Singular solution. --- Special case. --- Special functions. --- Summation. --- Theorem. --- Theory. --- Uniqueness theorem. --- Variable (mathematics). --- Without loss of generality.

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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 development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications.The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields.The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971).Originally published in 1975.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Fourier analysis. --- Local fields (Algebra) --- Fields, Local (Algebra) --- Algebraic fields --- Analysis, Fourier --- Mathematical analysis --- Corps algébriques --- Fourier analysis --- 511 --- 511 Number theory --- Number theory --- Local fields (Algebra). --- Harmonic analysis. Fourier analysis --- Fourier Analysis --- Abelian group. --- Absolute continuity. --- Absolute value. --- Addition. --- Additive group. --- Algebraic extension. --- Algebraic number field. --- Bessel function. --- Beta function. --- Borel measure. --- Bounded function. --- Bounded variation. --- Boundedness. --- Calculation. --- Cauchy–Riemann equations. --- Characteristic function (probability theory). --- Complex analysis. --- Conformal map. --- Continuous function. --- Convolution. --- Coprime integers. --- Corollary. --- Coset. --- Determinant. --- Dimension (vector space). --- Dimension. --- Dirichlet kernel. --- Discrete space. --- Distribution (mathematics). --- Endomorphism. --- Field of fractions. --- Finite field. --- Formal power series. --- Fourier series. --- Fourier transform. --- Gamma function. --- Gelfand. --- Haar measure. --- Haar wavelet. --- Half-space (geometry). --- Hankel transform. --- Hardy's inequality. --- Harmonic analysis. --- Harmonic function. --- Homogeneous distribution. --- Integer. --- Lebesgue integration. --- Linear combination. --- Linear difference equation. --- Linear map. --- Linear space (geometry). --- Local field. --- Lp space. --- Maximal ideal. --- Measurable function. --- Measure (mathematics). --- Mellin transform. --- Metric space. --- Modular form. --- Multiplicative group. --- Norbert Wiener. --- P-adic number. --- Poisson kernel. --- Power series. --- Prime ideal. --- Probability. --- Product metric. --- Rational number. --- Regularization (mathematics). --- Requirement. --- Ring (mathematics). --- Ring of integers. --- Scalar multiplication. --- Scientific notation. --- Sign (mathematics). --- Smoothness. --- Special case. --- Special functions. --- Subgroup. --- Subring. --- Support (mathematics). --- Theorem. --- Topological space. --- Unitary operator. --- Vector space. --- Analyse harmonique (mathématiques)

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An outrageous graphic novel that investigates key concepts in mathematicsIntegers and permutations-two of the most basic mathematical objects-are born of different fields and analyzed with different techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body.Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics.Travel with Detective von Neumann as he leaves no clue unturned, from shepherds' huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the pain as you work with our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all.Beautifully drawn and wittily and exquisitely detailed, Prime Suspects is unique, astonishing, and outrageous-a once-in-a-lifetime opportunity to experience mathematics like never before.

Mathematics --- Math --- Science --- Accuracy and precision. --- Alan Turing. --- Alexander Grothendieck. --- Analytic number theory. --- Anatoly Vershik. --- Arithmetic. --- Atle Selberg. --- Ben Green (mathematician). --- Bernhard Riemann. --- Bessel function. --- Big O notation. --- Binary logarithm. --- Bryna Kra. --- Calculation. --- Child prodigy. --- Coefficient. --- Comic book. --- Conjecture. --- Coprime integers. --- Cryptography. --- David Hilbert. --- Diagram (category theory). --- Diophantine geometry. --- Diophantus. --- Disquisitiones Arithmeticae. --- Emil Artin. --- Emmy Noether. --- Enrico Bombieri. --- Erica Klarreich. --- Felix Klein. --- Fermat's Last Theorem. --- Fields Medal. --- Friedrich Bessel. --- Fundamental theorem of arithmetic. --- Gamma function. --- Gauss sum. --- Gelfand. --- Grigori Perelman. --- Henri Cartan. --- Hermann Weyl. --- Hilbert's tenth problem. --- Integer. --- Jean-Pierre Serre. --- Joint probability distribution. --- Julia Robinson. --- Keith Devlin. --- Klaus Roth. --- Kloosterman sum. --- Language of mathematics. --- Logarithm. --- Log-log plot. --- Manjul Bhargava. --- Maryam Mirzakhani. --- Mathematical problem. --- Mathematical sciences. --- Mathematician. --- Mathematics. --- Men of Mathematics. --- Millennium Prize Problems. --- Modular form. --- Monic polynomial. --- Multiplication table. --- Natural logarithm. --- Natural number. --- Nicolas Bourbaki. --- Normal distribution. --- Number theory. --- Occam's razor. --- Oswald Veblen. --- Parity (mathematics). --- Permutation. --- Persi Diaconis. --- Peter Gustav Lejeune Dirichlet. --- Peter Scholze. --- Pierre Deligne. --- Pierre Samuel. --- Plus-minus sign. --- Poisson distribution. --- Polynomial. --- Prime factor. --- Prime number. --- Prime power. --- Probability theory. --- Proportionality (mathematics). --- Pure mathematics. --- Random permutation. --- Richard Dedekind. --- Riemann hypothesis. --- Riemann surface. --- Riemann zeta function. --- Robin Hartshorne. --- Saunders Mac Lane. --- Serge Lang. --- Shinichi Mochizuki. --- Siegel zero. --- Sieve theory. --- Sophie Germain. --- Stirling numbers of the first kind. --- Summation. --- Variable (mathematics).