Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms. II

DOI10.1215/S0012-7094-91-06422-7zbMath0760.58042OpenAlexW1531128757MaRDI QIDQ1190825

Allan Greenleaf, Gunther Uhlmann

Publication date: 27 September 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06422-7

zbMATH Keywords

\(X\)-ray transformcanonical relationssingular Fourier integral operators

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Integral operators (47G10) Integral geometry (53C65) Fourier integral operators applied to PDEs (35S30)

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Cites Work

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• Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms
• Fanning curves of Lagrangian manifolds and geodesic flows
• The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two
• Nonlocal inversion formulas for the X-ray transform
• Oscillatory integrals with singular symbols
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Lower dimensional integrability of \(L^2\) functions
• Complexes of straight lines in the space \(C^ n\)
• Fourier integral operators. I
• Estimates for singular Radon transforms and pseudodifferential operators with singular symbols
• The Structure of Rational and Ruled Symplectic 4-Manifolds
• Lagrangian Intersection and the Cauchy Problem
• Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121)
• On Matrices Whose Real Linear Combinations are Nonsingular

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