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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. --- Équations aux dérivées partielles --- Opérateurs pseudo-différentiels

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Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses.Originally published in 1978.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.

Geometric measure theory. --- Surfaces. --- Curvature. --- Measure theory --- Calculus --- Curves --- Surfaces --- Curved surfaces --- Geometry --- Shapes --- Affine transformation. --- Approximation. --- Asymptote. --- Barrier function. --- Besicovitch covering theorem. --- Big O notation. --- Bounded set (topological vector space). --- Boundedness. --- Calculation. --- Cauchy–Schwarz inequality. --- Characteristic function (probability theory). --- Compactness theorem. --- Completing the square. --- Concave function. --- Convex set. --- Convolution. --- Crystal structure. --- Curve. --- Derivative. --- Diameter. --- Differentiable function. --- Differentiable manifold. --- Differential geometry. --- Dimension. --- Domain of a function. --- Dyadic rational. --- Equivalence relation. --- Estimation. --- Euclidean space. --- Existential quantification. --- Exterior (topology). --- First variation. --- Gaussian curvature. --- Geometry. --- Grain boundary. --- Graph of a function. --- Grassmannian. --- Harmonic function. --- Hausdorff measure. --- Heat equation. --- Heat kernel. --- Heat transfer. --- Homotopy. --- Hypersurface. --- Hölder's inequality. --- Infimum and supremum. --- Initial condition. --- Lebesgue measure. --- Lebesgue point. --- Linear space (geometry). --- Lipschitz continuity. --- Mean curvature. --- Melting point. --- Microstructure. --- Monotonic function. --- Natural number. --- Nonparametric statistics. --- Order of integration (calculus). --- Order of integration. --- Order of magnitude. --- Parabolic partial differential equation. --- Paraboloid. --- Partial differential equation. --- Permutation. --- Perpendicular. --- Pointwise. --- Probability. --- Quantity. --- Quotient space (topology). --- Radon measure. --- Regularity theorem. --- Retract. --- Rewriting. --- Riemannian manifold. --- Right angle. --- Second derivative. --- Sectional curvature. --- Semi-continuity. --- Smoothness. --- Subsequence. --- Subset. --- Support (mathematics). --- Tangent space. --- Taylor's theorem. --- Theorem. --- Theory. --- Topology. --- Total curvature. --- Translational symmetry. --- Uniform boundedness. --- Unit circle. --- Unit vector. --- Upper and lower bounds. --- Variable (mathematics). --- Varifold. --- Vector field. --- Weight function. --- Without loss of generality.