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Analytical spaces --- 51 <082.1> --- Mathematics--Series --- Singular integrals --- Littlewood-Paley theory --- Calderón-Zygmund operator --- Elliptic operators --- Semigroups --- Intégrales singulières --- Littlewood-Paley, Théorie de --- Calderon-Zygmund, Opérateurs de --- Opérateurs elliptiques --- Semigroupes --- Calderón-Zygmund operator --- Integrals, Singular --- Integral operators --- Integral transforms --- Group theory --- Fourier analysis --- Functions of several real variables --- Differential operators, Elliptic --- Operators, Elliptic --- Partial differential operators --- Calderón-Zygmund singular integral operator --- Mikhlin-Calderon-Zygmund operator --- Operator, Calderón-Zygmund --- Singular integral operator, Calderón-Zygmund --- Zygmund-Calderón operator --- Linear operators --- Intégrales singulières. --- Littlewood-Paley, Théorie de. --- Calderon-Zygmund, Opérateurs de. --- Opérateurs elliptiques. --- Semigroupes.

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The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems.Originally published in 1979.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.

517.982.4 --- Pseudodifferential operators --- Operators, Pseudodifferential --- Pseudo-differential operators --- Theory of generalized functions (distributions) --- Pseudodifferential operators. --- 517.982.4 Theory of generalized functions (distributions) --- Operator theory --- Differential equations, Partial --- Équations aux dérivées partielles --- Opérateurs pseudo-différentiels --- Addition. --- Adjoint. --- Approximation. --- Asymptotic expansion. --- Banach space. --- Bounded operator. --- Boundedness. --- Calculation. --- Change of variables. --- Coefficient. --- Compact space. --- Complex analysis. --- Computation. --- Corollary. --- Cotangent bundle. --- Derivative. --- Differential operator. --- Disjoint union. --- Elliptic partial differential equation. --- Estimation. --- Euclidean distance. --- Euclidean vector. --- Existential quantification. --- Fourier integral operator. --- Fourier transform. --- Geometric series. --- Heat equation. --- Heisenberg group. --- Homogeneous distribution. --- Infimum and supremum. --- Integer. --- Integration by parts. --- Intermediate value theorem. --- Jacobian matrix and determinant. --- Left inverse. --- Linear combination. --- Linear map. --- Mean value theorem. --- Monograph. --- Monomial. --- Nilpotent group. --- Operator (physics). --- Operator norm. --- Order of magnitude. --- Orthogonal complement. --- Parametrix. --- Parity (mathematics). --- Partition of unity. --- Polynomial. --- Projection (linear algebra). --- Pseudo-differential operator. --- Quadratic function. --- Regularity theorem. --- Remainder. --- Requirement. --- Right inverse. --- Scientific notation. --- Self-reference. --- Several complex variables. --- Singular integral. --- Smoothness. --- Sobolev space. --- Special case. --- Submanifold. --- Subset. --- Sum of squares. --- Summation. --- Support (mathematics). --- Tangent space. --- Taylor's theorem. --- Theorem. --- Theory. --- Transpose. --- Triangle inequality. --- Uniform boundedness. --- Upper and lower bounds. --- Variable (mathematics). --- Without loss of generality. --- Zero set.

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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