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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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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