Geometry of pseudodifferential algebra bundles and Fourier integral operators
نویسندگان
چکیده
منابع مشابه
Geometry of Pseudodifferential Algebra Bundles and Fourier Integral Operators
We study the geometry and topology of (filtered) algebra-bundles ΨZ over a smooth manifold X with typical fibre ΨZ(Z;V ), the algebra of classical pseudodifferential operators of integral order on the compact manifold Z acting on smooth sections of a vector bundle V . First a theorem of Duistermaat and Singer is generalized to the assertion that the group of projective invertible Fourier integr...
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This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...
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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...
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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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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2017
ISSN: 0012-7094
DOI: 10.1215/00127094-0000013x