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 paradifferential operators.
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.
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In mathematical analysis, microlocalanalysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of...
1988/89 by Stephane Mallat and Yves Meyer and has predecessors in the microlocalanalysis in the theory of differential equations (the ironing method) and...
are closely related to ideas of Mikio Sato, on what he calls algebraic analysis. Important influences on the subject have been the technical requirements...
symplectic geometry, and he has also made contributions to the fields of microlocalanalysis, spectral theory, and mathematical physics. Guillemin obtained a...
linear differential operators, due to Lars Gårding, in the context of microlocalanalysis. Nonlinear differential equations are hyperbolic if their linearizations...
In mathematical analysis, more precisely in microlocalanalysis, the wave front (set) WF(f) characterizes the singularities of a generalized function...
Tokyo. Kashiwara made leading contributions towards algebraic analysis, microlocalanalysis, D-module theory, Hodge theory, sheaf theory and representation...
1949) is a Russian, Canadian mathematician who specializes in analysis, microlocalanalysis, spectral theory and partial differential equations. He is a...
sheaf of holomorphic functions on X to M. Hyperfunction D-module Microlocalanalysis Generalized function Edge-of-the-wedge theorem FBI transform Localization...
asymptotics, the crucial role was played by variational methods and microlocalanalysis. The extended Weyl law fails in certain situations. In particular...
geometry, for example in the formulation of the theory of D-modules and microlocalanalysis. Recently derived categories have also become important in areas...
sheaf theory. Further, it led to the theory of microfunctions and microlocalanalysis in linear partial differential equations and Fourier theory, such...
mathematician whose research focuses on inverse problems and imaging, microlocalanalysis, partial differential equations and invisibility. Uhlmann studied...
mathematician working in the areas of partial differential equations, microlocalanalysis, spectral theory and mathematical physics. He is currently a professor...
University of California, Berkeley. His mathematical interests include microlocalanalysis, scattering theory, and partial differential equations. He was an...
mathematician known for her work in mathematical analysis, and particularly in spectral geometry and microlocalanalysis. She is an associate professor of mathematics...
1961) is an American mathematician working in differential geometry, microlocalanalysis, and partial differential equations. He is currently a professor...
wave equations, and more generally for other hyperbolic equations. Microlocalanalysis Fourier transform Pseudodifferential operator Oscillatory integral...
applications in the fields of partial differential equations, geophysics, microlocalanalysis and general relativity so far. Colombeau algebras are named after...
the boundary of a convex body. A fuller understanding awaited the microlocalanalysis of the middle of the 20th century, The step from optics to dynamics...
In mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form T λ u ( x ) = ∫ R n e i λ S ( x...
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