Generalized oscillatory integrals and Fourier integral operators

Bounds for Singular Fractional Integrals and Related Fourier Integral Operators

Oscillatory and Fourier Integral Operators with Degenerate Canonical Relations

In (1.1) it is assumed that the real-valued phase function Φ is smooth in ΩL × ΩR where ΩL,ΩR are open subsets of R d and amplitude σ ∈ C 0 (ΩL × ΩR). (The assumption that dim(ΩL) = dim(ΩR) is only for convenience; many of the definitions, techniques and results described below have some analogues in the nonequidimensional setting.) The L boundedness properties of Tλ are determined by the geome...

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...

Curvelets 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.

Applications 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...