Related papers: Group Invariant Scattering
We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a smooth principal G-bundle. A `cylinder…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
Let $H$ be a locally compact group, $K$ be an LCA group, $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\tau$. In this…
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
Collective coherent scattering of laser light by an ensemble of polarizable point particles creates long range interactions, whose properties can be tailored by choice of injected laser powers, frequencies and polarizations. We use a…
We construct an invariant of the bi-Lipschitz contact equivalence of continuous function germs definable in a polynomially bounded o-minimal structure, such as semialgebraic functions. For a germ $f,$ the invariant is given in terms of the…
In this paper we generalize the geodesic flow on (finite) homogeneous graphs to a multiparameter flow on compact quotients of Euclidean buildings. Then we study the joint spectra of the associated transfer operators acting on suitable…
We give a definition of scattering matrices based on the asymptotic behaviors of generalized eigenfunctions and show that these scattering matrices are equivalent to the ones defined by wave-operator approach in long-range $N$-body…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
One can represent Schwartz distributions with values in a vector bundle $E$ by smooth sections of $E$ with distributional coefficients. Moreover, any linear continuous operator which maps $E$-valued distributions to smooth sections of…
We study mass preserving transport of passive tracers in the low-diffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonomous diffusion equation is approximated by that of a…
We consider an invariant quantum Hamiltonian $H=-\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a countable discrete symmetry group $\Gamma$. Typically, $\tilde{M}$ is the universal covering space of a…
We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…
We examine translation invariant operators on the Polyanalytic Sobolev-Fock spaces and show that they take the form \begin{align*} S_{\phi} F(z) = \int_{\mathbb{C}^n} F(w)e^{\pi z\cdot \overline{w}}\phi(w-z,\overline{w}-z) e^{\pi |w|^2}\,…
In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule…
Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the…
An SL-invariant extension of the concurrence to higher local Hilbert-space dimension is due to its relation with the determinant of the matrix of a $d\times d$ two qudits state, which is the only SL-invariant of polynomial degree $d$. This…
We investigate global solvability, in the framework of smooth functions and Schwartz distributions, of certain sums of squares of vector fields defined on a product of compact Riemannian manifolds $T \times G$, where $G$ is further assumed…
We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which…