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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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The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Harmonic analysis. --- Harmonic functions. --- Functions, Harmonic --- Laplace's equations --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Harmonic analysis. Fourier analysis --- Harmonic analysis --- Fourier analysis --- Harmonic functions --- Analyse harmonique --- Analyse de Fourier --- Fonctions harmoniques --- Fourier Analysis --- Fourier, Transformations de --- Euclide, Espaces d' --- Bessel functions --- Differential equations, Partial --- Fourier series --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Banach algebras --- Time-series analysis --- Analysis, Fourier --- Fourier analysis. --- Basic Sciences. Mathematics --- Analysis, Functions --- Analysis, Functions. --- Calculus --- Mathematical analysis --- Mathematics --- Fourier, Transformations de. --- Euclide, Espaces d'. --- Potentiel, Théorie du --- Fonctions harmoniques. --- Potential theory (Mathematics) --- Analytic continuation. --- Analytic function. --- Banach algebra. --- Banach space. --- Bessel function. --- Borel measure. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Cartesian coordinate system. --- Cauchy–Riemann equations. --- Change of variables. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Complex plane. --- Conformal map. --- Conjugate transpose. --- Continuous function (set theory). --- Continuous function. --- Convolution. --- Differentiation of integrals. --- Dimensional analysis. --- Dirichlet problem. --- Disk (mathematics). --- Distribution (mathematics). --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Function space. --- Green's theorem. --- Hardy's inequality. --- Hardy–Littlewood maximal function. --- Harmonic function. --- Hermitian matrix. --- Hilbert transform. --- Holomorphic function. --- Homogeneous function. --- Inequality (mathematics). --- Infimum and supremum. --- Interpolation theorem. --- Interval (mathematics). --- Lebesgue integration. --- Lebesgue measure. --- Linear interpolation. --- Linear map. --- Linear space (geometry). --- Line–line intersection. --- Liouville's theorem (Hamiltonian). --- Lipschitz continuity. --- Locally integrable function. --- Lp space. --- Majorization. --- Marcinkiewicz interpolation theorem. --- Mean value theorem. --- Measure (mathematics). --- Mellin transform. --- Monotonic function. --- Multiplication operator. --- Norm (mathematics). --- Operator norm. --- Orthogonal group. --- Paley–Wiener theorem. --- Partial derivative. --- Partial differential equation. --- Plancherel theorem. --- Pointwise convergence. --- Poisson kernel. --- Poisson summation formula. --- Polynomial. --- Principal value. --- Quadratic form. --- Radial function. --- Radon–Nikodym theorem. --- Representation theorem. --- Riesz transform. --- Scientific notation. --- Series expansion. --- Singular integral. --- Special case. --- Subharmonic function. --- Support (mathematics). --- Theorem. --- Topology. --- Total variation. --- Trigonometric polynomial. --- Trigonometric series. --- Two-dimensional space. --- Union (set theory). --- Unit disk. --- Unit sphere. --- Upper half-plane. --- Variable (mathematics). --- Vector space. --- Fourier, Analyse de --- Potentiel, Théorie du. --- Potentiel, Théorie du --- Espaces de hardy