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Fourier integral operators and the canonical operator
Russian Mathematical Surveys, 1981CONTENTS Introduction Chapter I. Real theory of Fourier integral operators ??1. Densities, pseudodifferential operators, and asymptotic expansions ??2. Homogeneous Lagrangian immersions ??3. The canonical operator ??4. Fourier integral operators ??5. Examples and applications Chapter II.
V. Nazaikinskii +3 more
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Mathematics of the USSR-Sbornik, 1981
On the basis of the stationary phase method for oscillatory integrals with complex phase function, the authors prove the coincidence of Fourier integral operators and Maslov's canonical operator. Bibliography: 17 titles.
Danilov, V. G., Le Vu An'
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On the basis of the stationary phase method for oscillatory integrals with complex phase function, the authors prove the coincidence of Fourier integral operators and Maslov's canonical operator. Bibliography: 17 titles.
Danilov, V. G., Le Vu An'
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Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities
Proceedings of the Edinburgh Mathematical Society, 2011This paper addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalized functions.
Claudia Garetto, M. Oberguggenberger
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Neural Operator: Learning Maps Between Function Spaces
arXiv.org, 2021The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map ...
Nikola B. Kovachki +6 more
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Quaternion fourier integral operators for spaces of generalized quaternions
Mathematical methods in the applied sciences, 2018This article aims to discuss a class of quaternion Fourier integral operators on certain set of generalized functions, leading to a method of discussing various integral operators on various spaces of generalized functions.
S. Al-Omari, D. Baleanu
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The Endpoint Estimate for Fourier Integral Operators
Acta Mathematica Scientia, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Guangqing, Yang, Jie, Chen, Wenyi
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Bilinear Fourier integral operators
Journal of Pseudo-Differential Operators and Applications, 2010The authors study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and Meyer via the introduction of an oscillating factor containing a real-valued phase of five variables \(\Phi(x,y_1,y_2,\xi_1,\xi_2)\) which is jointly
L. Grafakos, M. M. Peloso
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Representation of Fourier Integral Operators Using Shearlets
Journal of Fourier Analysis and Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K. Guo, D. Labate
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Regularity Properties of Fourier Integral Operators
The Annals of Mathematics, 1991The authors prove sharp \(L^ p\)-estimates for Fourier integral operators. Mainly the local theory is used. Also there are regularity results for solutions for the initial value problems for strictly hyperbolic partial differential equations \[ \begin{cases} Lu(x,t)=0, & t\neq 0,\\ \partial^ j_ tu|_{t=0}=f_ j(x), & 0\leq j\leq m-1,\end{cases} \] where \
Seeger, Andreas +2 more
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On Lp-boundedness of Fourier Integral Operators
Potential Analysis, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jie Yang, Guangqing Wang, Wenyi Chen
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