منابع مشابه
Bilinear Fourier Integral Operators
We 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 oscillatory factor containing a real-valued phase of five variables Φ(x, y1, y2, ξ1, ξ2) which is jointly homogeneous in the phase variables (ξ1, ξ2). For symbols of or...
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A recent body of work introduced new tight-frames of curvelets [3, 4] to address key problems in approximation theory and image processing. This paper shows that curvelets essentially provide optimally sparse representations of Fourier Integral Operators. Dedicated to Yves Meyer on the occasion of his 65th birthday.
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Fourier integral operators, for the calculus of which I refer to Hörmander [17], have been applied in essentially two ways: as similarity transformations and in the description of the solutions of genuinely nonelliptic (pseudo-) differential equations. The first application is based on the observation of Egorov [12] that if P9 resp. g, is a pseudo-differential operator with principal symbol equ...
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Fourier Integral Operators appear naturally in a variety of problems related to hyperbolic partial differential equations. While wavelets and other traditional time-frequency methods have been successfully employed for representing many classes of singular integral operators, these methods are not equally effective in dealing with Fourier Integral Operators. In this paper, we show that the shea...
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We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically a so-called Fourier integral operator (FIO) of the form ∫ ea(x, ξ) f̂(ξ)dξ at points given on a Cartesian grid. Here, ξ is a frequency variable, f̂(ξ) is the F...
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1972
ISSN: 0001-5962
DOI: 10.1007/bf02392165