Related papers: Global L2-Boundedness Theorems for Semiclassical F…
We establish a characterization of complex linear canonical transformations that are positive with respect to a pair of strictly plurisubharmonic quadratic weights. As an application, we show that the boundedness of a class of Toeplitz…
We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global $L^p$-boundedness for a class of Fourier integral operators. While the local…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
We consider a class of Fourier integral operators, globally defined on $\mathbb{R}^{d}$, with symbols and phases satisfying product type estimates (the so-called $SG$ or scattering classes). We prove a sharp continuity result for such…
We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schr\"odinger…
As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also…
The problem of quantizing the canonical pair angle and action variables phi and I is almost as old as quantum mechanics itself and since decades a strongly debated but still unresolved issue in quantum optics. The present paper proposes a…
We study continuity properties in Lebesgue spaces for a class of Fourier integral operators arising in the study of the Boltzmann equation. The phase has a H\"older-type singularity at the origin. We prove boundedness in $L^1$ with a…
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…
We establish global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on product of $L^p$ spaces by proving endpoint boundedness on suitable products spaces containing combinations of the…
In this paper, we give an example of Fourier integral operator with a symbol belongs to $\bigcap\limits_{0<\rho <1}S_{\rho,1}^{0}$ that cannot be extended as a bounded operator on $L^{2}(\mathbb{R}^{n}).$
We illustrate the composition properties for an extended family of SG Fourier integral operators. We prove continuity results for operators in this class with respect to $L^2$ and weighted modulation spaces, and discuss continuity on…
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for…
The aim of this paper is to give a review of local and global properties of Fourier integral operators with real and complex phases, in local $L^p$, global $L^2$, and in Colombeau's spaces.
In this paper we develop elements of the global calculus of Fourier integral operators in $R^n$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev $L^2$ estimates for a class of Fourier…
We link Sogge's type $L^p$-estimates for eigenfunctions of the Laplacian on compact manifolds with the problem of providing criteria for the $r$-nuclearity of Fourier integral operators. The classes of Fourier integral operators…
In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter H\"ormander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase…
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the…
In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…
While the local $L^p$-boundedness of nondegeneral Fourier integral operators is known from the work of Seeger, Sogge and Stein, not so many results are available for the global boundedness on $L^p(\mathbb R^n)$. In this paper we give a…