Results 11 to 20 of about 277,415 (327)
A Class of Unbounded Fourier Integral Operators
Journal of Mathematical Analysis and Applications, 1998 INTRODUCTION The theory of pseudodifferential operators is well suited for investigating various problems connected with elliptic differential equations. However, this theory fails to be adequate for studying equations of hyperbolic type, and one is then forced to examine a wider class of operators, the Ž w x. so-called Fourier integral operators see 1,
Mahir Hasanov
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Local Formula for the Index of a Fourier Integral Operator [PDF]
Journal of Differential Geometry, 2000 We show that the index of an elliptic Fourier integral operator associated to a contact diffeomorphism $\phi$ of cosphere bundles of two Riemannian manifolds X and Y is given by $\int_{B^*X}\hat{A}(T^*X)\exp{\theta} - \int_{B^*Y}\hat{A}(T^*Y)\exp{\theta}$
E. Leichtnam, R. Nest, B. Tsygan
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The weak-type $(1,1)$ of Fourier integral operators of order $-(n-1)/2$ [PDF]
Journal of the Australian Mathematical Society, 2002 Let T be a Fourier integral operator on Rn of order–(n–1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1).
Terence Tao
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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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Local smoothing of Fourier integral operators and Carleson-Sjölin estimates [PDF]
, 1993 The purpose of this paper is twofold. First, if Y and Z are smooth paracompact manifolds of dimensions n ~ 2 and n + 1 , respectively, we shall prove local regularity theorems for a certain class of Fourier integral operators !T E /f1.(Z , Y; ~) which ...
Gerd Mockenhaupt +2 more
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Integral operators, bispectrality and growth of Fourier algebras [PDF]
Journal für die Reine und Angewandte Mathematik, 2018 In the mid 1980s it was conjectured that every bispectral meromorphic function ψ ( x , y ) {\psi(x,y)} gives rise to an integral operator K ψ ( x , y ) {K_{\psi}(x,y)} which possesses a commuting differential operator.
W. Riley Casper, Milen Yakimov
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Approximation of Fourier Integral Operators by Gabor Multipliers [PDF]
Journal of Fourier Analysis and Applications, 2011 A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth phase and a ...
E. Cordero, K. Gröchenig, F. Nicola
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On Fourier integral operators with Hölder-continuous phase [PDF]
Analysis and Applications, 2018 We study continuity properties in Lebesgue spaces for a class of Fourier integral operators arising in the study of the Boltzmann equation. The phase has a Hölder-type singularity at the origin. We prove boundedness in [Formula: see text] with a precise loss of decay depending on the Hölder exponent, and we show by counterexamples that a loss occurs ...
Elena Cordero, Fabio Nicola, Eva Primo
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A Class of Fourier Integral Operators on Manifolds with Boundary [PDF]
, 2014 We study a class of Fourier integral operators on compact manifolds with boundary X and Y , associated with a natural class of symplectomorphisms \(\mathcal{X} :\;T^{*}Y \; \backslash \;0\rightarrow\;T^{*}X\; \backslash \;0\), namely, those which ...
U. Battisti, S. Coriasco, E. Schrohe
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Fourier-Like Multipliers and Applications for Integral Operators [PDF]
Complex Analysis and Operator Theory, 2017 Timelimited functions and bandlimited functions play a fundamental role in signal and image processing. But by the uncertainty principles, a signal cannot be simultaneously time and bandlimited.
Saifallah Ghobber
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