Related papers: Global L2-Boundedness Theorems for Semiclassical F…

We define the domain of a linear fractional transformation in a space of operators and show that both the affine automorphisms and the compositions of symmetries act transitively on these domains. Further, we show that Liouville's theorem…

We prove a boundedness criterion for a class of dyadic multilinear forms acting on two-dimensional functions. Their structure is more general than the one of classical multilinear Calder\'{o}n-Zygmund operators as several functions can now…

Let $T^n$ denote the n-dimensional torus. The class of the bounded operators on $L^2(T^n)$ with analytic orbit under the action of $T^n$ by conjugation with the translation operators is shown to coincide with the class of the zero-order…

In this note, we consider a Fourier integral operator defined by \begin{align*} T_{\phi,a}f(x) = \int_{\mathbb{R}^{n}}e^{i\phi(x,\xi)}a(x,\xi)\widehat{f} \xi)d\xi, \end{align*}here $a$ is the amplitude, and $\phi$ is the phase. Let…

In this paper, we consider the $L^2$-boundedness of pseudo-differential operators with symbols in $\alpha$-modulation spaces.

Global quantization of pseudo-differential operators on compact Lie groups is introduced relying on the representation theory of the group rather than on expressions in local coordinates. Operators on the 3-dimensional sphere and on group…

A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…

We give explicit necessary and sufficient conditions for the boundedness of the general second order differential operator L with real- or complex-valued distributional coefficients acting from the Sobolev space W^{1,2}(R^n) to its dual…

Any bounded linear operator $ T $ on $ L^2(\mathbb{R}^n) $ gives rise to the operator $ S= B \circ T \circ B^\ast $ on the Fock space $ \mathcal{F}(\C^n) $ where $ B $ is the Bargmann transform. In this article we identify those $ S $ which…

We study semiclassical Gevrey pseudodifferential operators, acting on exponentially weighted spaces of entire holomorphic functions. The symbols of such operators are Gevrey functions defined on suitable I-Lagrangian submanifolds of the…

We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, we study the uniqueness of strongly irreducible…

Inspired by a recent article \cite[JFAA, 28(2):1-34, (2022)]{Skrettingland2022JoFAaA}, this paper is devoted to the study of suitable window class in the framework of bounded linear operators on $L^2(\rd)$. We establish a natural and…

We give an exposition on the $L^2$ theory of the perturbed Fourier transform associated with a Schr\"odinger operator $H=-d^2/dx^2 +V$ on the real line, where $V$ is a real-valued \mbox{finite} measure. In the case $V\in L^1\cap L^2$, we…

We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable…

An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {\phi_k}_{k=0}^{\infty} such that L\phi_k=0 for k=0,1, L\phi_k=k(k-1)\phi_{k-2}, for k=2,3,... and all \phi_k satisfy…

We use Fourier Neural Operators (FNOs) to study the relation between the modulus and phase of amplitudes in $2\to 2$ elastic scattering at fixed energies. Unlike previous approaches, we do not employ the integral relation imposed by…

A typical classical interference pattern of two waves with intensities I_1, I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3 observables p = sqrt{I_1 I_2}, p cos\phi and -p sin\phi. They are, e.g. the starting point…

A complex function is associated to each bounded linear operator

This article presents an investigation of global properties of a class of differential operators on $\mathbb{T}^1\times\mathbb{R}$. Our approach involves the utilization of a mixed Fourier transform, incorporating both partial Fourier…

Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…