Fourier integral operators and the canonical operator

DOI10.1070/RM1981v036n02ABEH002599zbMath0507.58043OpenAlexW1982228754MaRDI QIDQ4745032

B. Yu. Sternin, Victor G. Oshmyan, Vladimir E. Nazaikinskii, Victor Shatalov

Publication date: 1981

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm1981v036n02abeh002599

zbMATH Keywords

complex-valued phase functionshomogeneous Lagrangian immersionsHörmander's theory of Fourier integral operatorsMaslov's theory of canonical operators

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Integral operators (47G10) Fourier integral operators applied to PDEs (35S30) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20)

Related Items (12)

Maslov's canonical operator in arbitrary coordinates on the Lagrangian manifold ⋮ Class of Fredholm Boundary Value Problems for the Wave Equation with Conditions on the Entire Boundary ⋮ Traces of quantized canonical transformations localized on a finite set of points ⋮ Traces of quantized canonical transformations on submanifolds and their applications to Sobolev problems with nonlocal conditions ⋮ On traces of Fourier integral operators on submanifolds ⋮ Elliptic \(\mathbb{Z}\)-operators associated with the metaplectic group ⋮ Elliptic operators associated with groups of quantized canonical transformations ⋮ Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations ⋮ Electronic optics in graphene in the semiclassical approximation ⋮ Maslov's canonical operator in problems on localized asymptotic solutions of hyperbolic equations and systems ⋮ Elliptic operators associated with groups of quantized canonical transformations ⋮ Asymptotic approximations for the phase space Schrödinger equation

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