Related papers: Calculus for Fourier Integral Operators in general…
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…
We prove sharp endpoint results for the Fourier restriction operator associated to nondegenerate curves in $\Bbb R^d$, $d\ge 3$, and related estimates for oscillatory integral operators. Moreover, for some larger classes of curves in $\Bbb…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…
Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…
We proof pointwise bounds for rough Fourier integral operators by the $L^p$ Hardy-Littlewood maximal function. We assume the Fourier integral operators have amplitudes in $L^\infty S^m_\rho$ and phases $\varphi$ such that $\varphi(x,\xi) -…
Basic properties of Fourier integral operators on the torus are studied by using the global representations by Fourier series instead of local representations. The results can be applied to weakly hyperbolic partial differential equations.
It is well known that the matrix of a metaplectic operator with respect to phase-space shifts is concentrated along the graph of a linear symplectic map. We show that the algebra generated by metaplectic operators and by pseudodifferential…
We construct solutions to the eikonal equation for a class of long-range potentials, derive strong radiation condition bounds for the corresponding Schr\"odinger operator and apply them to construct the generalized Fourier transform,…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
We show that the scattering matrix for a class of Schr\"odinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the generating function of the modified classical scattering map.
Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\log$-homogeneous distribution as an approach to $\zeta$-functions for a class of Fourier Integral Operators which includes cases of…
For $g \in \operatorname{Hol}(\mathbb D)$, we study the class of generalized integration operators $T_{g,a}$, acting on Hardy and Bergman spaces of the unit disc in the complex plane. This class of integral operators were introduced to…
We introduce the notion of Schr\"odinger integral operators and prove sharp local and global regularity results for these (including propagators for the quantum mechanical harmonic oscillator). Furthermore we introduce general classes of…
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…
Volterra companion integral and multiplication operators with holomorphic symbols are studied for a large class of generalized Fock spaces on the complex plane $\CC$. The weights defining these spaces are radial and subject to a mild…
Operators with continuous spectra naturally arise in spectral theory, quantum mechanics, automorphic forms, and noncommutative geometry. However, analyzing such operators, particularly in the non-selfadjoint setting, remains challenging due…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
We push the definition of multiple operator integrals (MOIs) into the realm of unbounded operators, using the pseudodifferential calculus from the works of Connes and Moscovici, Higson, and Guillemin. This in particular provides a natural…
Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems of the Loewy-Ore theory of factorization…
In this paper, we present a complete spectral research of generalized Ces\`aro operators on Sobolev-Lebesgue sequence spaces. The main idea is to subordinate such operators to suitable $C_0$-semigroups on these sequence spaces. We introduce…