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This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.

Waves --- Scattering (Physics) --- Perturbation (Mathematics) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Mathematics. --- Scattering --- Acoustic wave equation. --- Acoustic wave. --- Affine space. --- Angular frequency. --- Approximation. --- Asymptotic analysis. --- Asymptotic expansion. --- Banach space. --- Basis (linear algebra). --- Bessel's inequality. --- Boundary value problem. --- Bounded operator. --- C0-semigroup. --- Calculation. --- Characteristic function (probability theory). --- Classical physics. --- Codimension. --- Coefficient. --- Continuous function (set theory). --- Continuous function. --- Continuous spectrum. --- Convolution. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dirac delta function. --- Dirichlet problem. --- Distribution (mathematics). --- Duhamel's principle. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Electromagnetism. --- Equation. --- Existential quantification. --- Exponential function. --- Floquet theory. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fredholm integral equation. --- Frequency domain. --- Helmholtz equation. --- Hilbert space. --- Initial value problem. --- Integral equation. --- Integral transform. --- Integration by parts. --- Inverse problem. --- Inverse scattering problem. --- Lebesgue measure. --- Linear differential equation. --- Linear map. --- Linear space (geometry). --- Locally integrable function. --- Longitudinal wave. --- Mathematical analysis. --- Mathematical physics. --- Metric space. --- Operator theory. --- Ordinary differential equation. --- Orthonormal basis. --- Orthonormality. --- Parseval's theorem. --- Partial derivative. --- Partial differential equation. --- Phase velocity. --- Plane wave. --- Projection (linear algebra). --- Propagator. --- Quantity. --- Quantum mechanics. --- Reflection coefficient. --- Requirement. --- Riesz representation theorem. --- Scalar (physics). --- Scattering theory. --- Scattering. --- Scientific notation. --- Self-adjoint operator. --- Self-adjoint. --- Series expansion. --- Sine wave. --- Spectral method. --- Spectral theorem. --- Spectral theory. --- Square-integrable function. --- Subset. --- Theorem. --- Theory. --- Time domain. --- Time evolution. --- Unbounded operator. --- Unitarity (physics). --- Vector space. --- Volterra integral equation. --- Wave function. --- Wave packet. --- Wave propagation.

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Here Michael Taylor develops pseudodifferential operators as a tool for treating problems in linear partial differential equations, including existence, uniqueness, and estimates of smoothness, as well as other qualitative properties.Originally published in 1981.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.

Differential equations, Partial. --- Pseudodifferential operators. --- Airy function. --- Antiholomorphic function. --- Asymptotic expansion. --- Banach space. --- Besov space. --- Bessel function. --- Big O notation. --- Bilinear form. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Canonical transformation. --- Cauchy problem. --- Cauchy–Kowalevski theorem. --- Cauchy–Riemann equations. --- Change of variables. --- Characteristic variety. --- Compact operator. --- Constant coefficients. --- Continuous linear extension. --- Convex cone. --- Differential operator. --- Dirac delta function. --- Discrete series representation. --- Distribution (mathematics). --- Egorov's theorem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eikonal equation. --- Elliptic operator. --- Equation. --- Existence theorem. --- Existential quantification. --- Formal power series. --- Fourier integral operator. --- Fourier inversion theorem. --- Fubini's theorem. --- Fundamental solution. --- Hardy–Littlewood maximal function. --- Harmonic conjugate. --- Heaviside step function. --- Hilbert transform. --- Holomorphic function. --- Homogeneous function. --- Hyperbolic partial differential equation. --- Hypersurface. --- Hypoelliptic operator. --- Hölder condition. --- Inclusion map. --- Infimum and supremum. --- Initial value problem. --- Integral equation. --- Integral transform. --- Integration by parts. --- Interpolation space. --- Lebesgue measure. --- Linear map. --- Lipschitz continuity. --- Lp space. --- Marcinkiewicz interpolation theorem. --- Maximum principle. --- Mean value theorem. --- Modulus of continuity. --- Mollifier. --- Norm (mathematics). --- Open mapping theorem (complex analysis). --- Open set. --- Operator (physics). --- Operator norm. --- Orthonormal basis. --- Parametrix. --- Partial differential equation. --- Partition of unity. --- Polynomial. --- Probability measure. --- Projection (linear algebra). --- Pseudo-differential operator. --- Riemannian manifold. --- Self-adjoint operator. --- Self-adjoint. --- Singular integral. --- Skew-symmetric matrix. --- Smoothness. --- Sobolev space. --- Special case. --- Spectral theorem. --- Spectral theory. --- Support (mathematics). --- Symplectic vector space. --- Taylor's theorem. --- Theorem. --- Trace class. --- Unbounded operator. --- Unitary operator. --- Vanish at infinity. --- Vector bundle. --- Wave front set. --- Weierstrass preparation theorem. --- Wiener's tauberian theorem. --- Zero of a function.

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This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Harmonic analysis. Fourier analysis --- Phase space (Statistical physics) --- Harmonic analysis --- 512.54 <043> --- 530.145 <043> --- 517.986.6 --- 51-7 <043> --- 517.986.6 <043> --- Groups. Group theory--Dissertaties --- Quantum theory--Dissertaties --- Harmonic analysis of functions of groups and homogeneous spaces --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc.--Dissertaties --- Harmonic analysis of functions of groups and homogeneous spaces--Dissertaties --- 517.986.6 <043> Harmonic analysis of functions of groups and homogeneous spaces--Dissertaties --- 51-7 <043> Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc.--Dissertaties --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- 530.145 <043> Quantum theory--Dissertaties --- 512.54 <043> Groups. Group theory--Dissertaties --- Space, Phase (Statistical physics) --- Generalized spaces --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Harmonic analysis. --- Analytic continuation. --- Analytic function. --- Antisymmetric tensor. --- Asymptotic expansion. --- Automorphism. --- Bilinear form. --- Bounded operator. --- Calculation. --- Canonical commutation relation. --- Canonical transformation. --- Cauchy–Riemann equations. --- Cayley transform. --- Class function (algebra). --- Classical mechanics. --- Commutative property. --- Complex analysis. --- Configuration space. --- Differential equation. --- Differential geometry. --- Differential operator. --- Eigenvalues and eigenvectors. --- Equation. --- Explicit formula. --- Fock space. --- Fourier analysis. --- Fourier integral operator. --- Fourier transform. --- Functional analysis. --- Gaussian function. --- Gaussian integral. --- Geometric quantization. --- Hamiltonian mechanics. --- Hamiltonian vector field. --- Heisenberg group. --- Hermite polynomials. --- Hermitian symmetric space. --- Hilbert space. --- Hilbert transform. --- Integral transform. --- Invariant subspace. --- Irreducible representation. --- Lebesgue measure. --- Lie algebra. --- Lie superalgebra. --- Lie theory. --- Mathematical physics. --- Number theory. --- Observable. --- Ordinary differential equation. --- Orthonormal basis. --- Oscillator representation. --- Oscillatory integral. --- Partial differential equation. --- Phase factor. --- Phase space. --- Point at infinity. --- Poisson bracket. --- Polynomial. --- Power series. --- Probability. --- Projection (linear algebra). --- Projective Hilbert space. --- Projective representation. --- Projective space. --- Pseudo-differential operator. --- Pullback (category theory). --- Quadratic function. --- Quantum harmonic oscillator. --- Quantum mechanics. --- Representation theory. --- Schrödinger equation. --- Self-adjoint operator. --- Semigroup. --- Several complex variables. --- Siegel disc. --- Sobolev space. --- Spectral theorem. --- Spectral theory. --- State-space representation. --- Stone's theorem. --- Stone–Weierstrass theorem. --- Summation. --- Symmetric space. --- Symmetric tensor. --- Symplectic geometry. --- Symplectic group. --- Symplectic vector space. --- Symplectomorphism. --- Tangent space. --- Tangent vector. --- Theorem. --- Translational symmetry. --- Unbounded operator. --- Unit vector. --- Unitarity (physics). --- Unitary operator. --- Unitary representation. --- Variable (mathematics). --- Wave packet.