Results 11 to 20 of about 3,272 (305)
On a Class of h-Fourier Integral Operators
Demonstratio Mathematica, 2014 In this paper, we study the L2-boundedness and L2-compactness of a class of h-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to 0).
Harrat Chahrazed +1 more
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Fourier integral operators. I [PDF]
Acta Mathematica, 1971 Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value is rather limited in genuinely non-elliptic problems. In this paper we shall therefore discuss some more general classes of operators which are adapted to
Lars Hörmander
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Fourier integral operators. II [PDF]
Acta Mathematica, 1972 J. J. Duistermaat, Lars Hörmander
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L1-boundedness of rough Fourier integral operators. [PDF]
Journal of Pseudo-Differential Operators and Applications, 2022 Abstract In this paper, we study the L1-boundedness of Fourier integral operator T_{\phi,a} with rough symbol a\in L^{\infty}S^{m}_{\rho} and a new class of rough phase \phi. In this class, we extend the L^{\infty}\phi^{2} and non-degeneracy conditions to some generalized derivative estimation and some measure condition respectively.
Joachim Sindayigaya
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Schatten class Fourier integral operators [PDF]
Applied and Computational Harmonic Analysis, 2010 Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier integral operator has a smooth phase function and its symbol is well-localized in time and frequency, then the operator
Shannon Bishop
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Generalized oscillatory integrals and Fourier integral operators [PDF]
Proceedings of the Edinburgh Mathematical Society, 2009 AbstractIn this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential
Claudia Garetto +2 more
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Rough Pseudodifferential Operators on Hardy Spaces for Fourier Integral Operators II [PDF]
Journal of Fourier Analysis and Applications, 2022 AbstractWe obtain improved bounds for pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $$a(x,\eta )$$ a ( x , η ) are ...
Jan Rozendaal
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Magnetic Fourier integral operators [PDF]
Journal of Pseudo-Differential Operators and Applications, 2011 In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral Operators Theory to the case with a magnetic field, proving composition theorems, continuity theorems in 'magnetic ...
Iftimie, Viorel, Purice, Radu
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Fourier integrals operators on lie groupoids [PDF]
Advances in Mathematics, 2016 As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also identify those Lagrangian which correspond to equivariant families parametrized by the unit space G (0) of homogeneous ...
Jean-Marie Lescure, Stéphane Vassout
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On Fourier Integral Operators [PDF]
Proceedings of the American Mathematical Society, 1982 We consider operators of the form: ∫ − ∞ ∞ F t φ ( t ) d t \int _{ - \infty }^\infty {{F_t}\varphi (t)\;dt} , where
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