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Lectures on Pseudo-Differential Operators

Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24)

Elias M. Stein, Alexander Nagel

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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.

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Schlagwörter

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