Related papers: The Light Ray transform on Lorentzian manifolds

We study the effect of a splitting operator S_t on the L^p norm of the Fourier transform of a function f and on the operator norm of a Fourier multiplier m. Most of our results assume p is an even integer, and are often stronger when f or m…

We explore the Fourier transform of the Heegaard Floer $d$-invariants, which is particularly well-behaved with respect to connected sum. As corollaries, we show that lens spaces are cancellable in the monoid of 3-manifolds up to integer…

It is well-known that a torsion-free linear connection on a light-like manifold $(M,g)$ compatible with the degenerate metric $g$ exists if and only if $Rad(TM)$ is a Killing distribution. In case of existence, there is an infinitude of…

For semilinear wave equations on Lorentzian manifolds with quadratic derivative non-linear terms, we study the inverse problem of determining the background Lorentzian metric. Under some conditions on the nonlinear term, we show that from…

We investigate the $M1$ radiative transitions between light vector $\mathcal{V}$ and pseudoscalar $\mathcal{P}$ mesons in the 1S and 2S states in the light-front quark model. To this end, we use the light-front wave functions (LFWFs)…

Via a functor from certain Lorentzian to Riemannian manifolds, we obtain a finiteness result.

The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…

We introduce the following linear combination interpolation problem (LCI): Given $N$ distinct numbers $w_1,\ldots w_N$ and $N+1$ complex numbers $a_1,\ldots, a_N$ and $c$, find all functions $f(z)$ analytic in a simply connected set…

This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.

Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…

Let $M^{n+1}_1$ be a light-like geodesically complete Lorentzian $(n+1)$-manifold satisfying the null energy condition. We show that null hypersurfaces properly immersed in $M^{n+1}_1$ are totally geodesic.

We point out that the geometry of connected totally geodesic compact null hypersurfaces in Lorentzian manifolds is only slightly more specialized than that of Riemannian flows over compact manifolds, the latter mathematical theory having…

We study spectral properties of the transfer operators $L$ defined on the circle $\mathbb T=\mathbb R/\mathbb Z$ by $$(Lu)(t)=\frac{1}{d}\sum_{i=0}^{d-1} f\left(\frac{t+i}{d}\right)u\left(\frac{t+i}{d}\right),\ t\in\mathbb T$$ where $u$ is…

In this paper we prove weighted mixed norm estimates for Riesz transforms associated to Hermite and special Hermite operators. The estimates are shown to be equivalent to vectorvalued esimates for a sequence of operators defined in terms of…

We present a reconstruction of the Lagrangian for $f(R)$ gravity by using a massive scalar field. The scalar field is minimally coupled to the action of $f(R)$ gravity. We demonstrate the use of a theorem based on invertible point…

Light Field (LF) offers unique advantages such as post-capture refocusing and depth estimation, but low-light conditions limit these capabilities. To restore low-light LFs we should harness the geometric cues present in different LF views,…

This article contains a characterization of when certain weighted Sobolev spaces on $\Bbb R^n$ embed compactly into $L^2(\mathbb R^n, \varphi)$. The characterization is in terms of derivatives of the weight function $\varphi$ and involves…

We consider restricted light ray transforms arising from an inverse problem of finding cosmic strings. We construct a relative left parametrix for the transform on two tensors, which recovers the space-like and some light-like singularities…

Introducing a notion of the weighted mean sigma-r curvature and using the weighted Newton transformations we derive in this paper some integral formulae on weighted manifolds. These formulae generalize the flux formula and some of its…

Many stochastic processes are defined on special geometrical objects like spheres and cones. We describe how tools from harmonic analysis, i.e. Fourier analysis on groups, can be used to investigate probability density functions (pdfs) on…