Fourier analysis | Generalized functions | Microlocal analysis

Microlocal analysis

In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes generalized functions, pseudo-differential operators, wave front sets, Fourier integral operators, oscillatory integral operators, and . The term microlocal implies localisation not only with respect to location in the space, but also with respect to cotangent space directions at a given point. This gains in importance on manifolds of dimension greater than one. (Wikipedia).

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Related pages

Wave front set | Oscillatory integral operator | Manifold | Cotangent space | Dimension | Generalized function | Partial differential equation | Fourier integral operator | Algebraic analysis | Fourier transform | Pseudo-differential operator | Mathematical analysis