Exponentially sparse representations of Fourier integral operators
نویسندگان
چکیده
منابع مشابه
Sparse Shearlet Representation of Fourier Integral Operators
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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This technical report is a companion to [4]. We prove that Fourier Integral Operators admit ‘optimally’ sparse representations in curvelet frames. We give all the necessary definitions and notations for the discussion to be self-contained.
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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...
متن کاملApplications of Fourier Integral Operators
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...
متن کاملCurvelets and Fourier Integral Operators
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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ژورنال
عنوان ژورنال: Revista Matemática Iberoamericana
سال: 2015
ISSN: 0213-2230
DOI: 10.4171/rmi/841