h-Fourier Integral Operators with Complex Phase

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...

Fourier Integral Operators with Cusp Singularities

Fourier Integral Operators with Fold Singularities

We shall be concerned with Lα → Lqβ mapping properties of operators in I(X,Y ; C′) (here Lqβ denotes the L q Sobolev space). These are well known in case that C is locally the graph of a canonical transformation; this means that the projections πL : C → T X, πR : C → T Y are locally diffeomorphisms. In particular dX = dY := d. Then F ∈ I(X,Y, C′) maps Lα,comp(Y ) into Lβ,loc(X) if β ≤ α−μ. This...

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...