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$L^p$ to $L^p_{\beta}$ boundedness theorems are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional…
We study the theory of scattering for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling,in space dimension 3.We prove in particular the existence of modified wave operators for that system with…
We provide a simple sufficient condition in an abstract framework to deduce the existence and completeness of wave operators (resp. modified wave operators) on Sobolev spaces from the existence and completeness of the usual wave operators…
We prove that for the mass critical nonlinear Schrodinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the one-dimensional case,…
Denote by $L_D$ the Sturm-Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$ with Dirichlet boundary conditions $y(0)=y(\pi)=0$. Let $\{\lambda_k\}_1^\infty$ and $\{\alpha_k\}_1^\infty$ be the sequences of the eigenvalues…
I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order $2$. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the $L^2$-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together…
We study formal series which are invariants of plumbed 3-manifolds twisted by root lattices. These series extend the BPS $q$-series $\widehat{Z}(q)$ recently defined in Gukov-Pei-Putrov-Vafa, Gukov-Manolescu, Park, and further refined in…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
The shallow-water system is a standard model for long waves in shallow water. The system is hyperbolic and, for a large class of initial data, solutions develop steep gradients leading to shock formation in finite time. Since such…
We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving…
In this paper, we study an inverse scattering problem at fixed energy on three-dimensional asymptotically hyperbolic St{\"a}ckel manifolds having the topology of toric cylinders and satisfying the Robertson condition. On these manifolds the…
The aim of this paper is to derive a new uncertainty principle for the generalized $q$-Bessel wavelet transform studied earlier in \cite{Rezguietal}. In this paper, an uncertainty principle associated with wavelet transforms in the…
We introduce a new class which generalizes the class of B-Weyl operators. We say that $T\in L(X)$ is pseudo B-Weyl if $T=T_1\oplus T_2$ where $T_1$ is a Weyl operator and $T_2$ is a quasi-nilpotent operator. We show that the corresponding…
A wavelet basis is a basis for the $K$-Banach space $C(R, K)$ of continuous functions from a complete discrete valuation ring $R$ whose residue field is finite to its quotient field $K$. In this paper, we prove a characterization of…
In a recent article, Arendt and ter Elst have shown that every sectorial form is in a natural way associated with the generator of an analytic strongly continuous semigroup, even if the form fails to be closable. As an intermediate step…
In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and…