Related papers: Nonembeddability theorems via Fourier analysis

The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…

We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erd\H os, which says that the number of distances determined by $n$ points in ${\Bbb R}^d$ is at least $C_d…

We study the observability of the one-dimensional Schr{\"o}dinger equation and of the beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series,…

We study the low energy effective theory for a non-Fermi liquid state in 2+1 dimensions, where a transverse U(1) gauge field is coupled with a patch of Fermi surface with N flavors of fermion in the large N limit. In the low energy limit,…

Consider symmetric simple exclusion processes, with or without Glauber dynamics on the boundary set, on a sequence of connected unweighted graphs $G_N=(V_N,E_N)$ which converge geometrically and spectrally to a compact connected metric…

In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle…

In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new…

The unit distance embeddability of a graph, like planarity, involves a mix of constraints that are combinatorial and geometric. We construct a unit distance embedding for $H-e$ in the hope that it will lead to an embedding for $H$. We then…

Wasserstein distances form a family of metrics on spaces of probability measures that have recently seen many applications. However, statistical analysis in these spaces is complex due to the nonlinearity of Wasserstein spaces. One…

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…

We study the Erdos distance conjecture on the unit sphere in three dimensions using Fourier analytic methods.

We introduce an amalgam type space, a subspace of $L^1(\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the…

We prove a non-vanishing result of modular L-values with quadratic twists, where the quadratic discriminants are in a short interval. Using this fact and Waldspurger's theorem, we improve the results of Balog-Ono[The chebotarev density…

We use unoriented versions of instanton and knot Floer homology to prove inequalities involving the Euler characteristic and the number of local maxima appearing in unorientable cobordisms, which mirror results of a recent paper by Juhasz,…

We prove several incidence theorems in vector spaces over finite fields using bounds for various classes of exponential sums and apply these to Erdos-Falconer type distance problems.

We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit…

Fermionic linear optics (FLO) with Gaussian resources is efficiently classically simulable. We show that this is no longer the case for such quantum circuits for fermions with internal degrees of freedom, equipped with mid-circuit number…

The angle resolved photoemission spectroscopy lineshapes of quasi one-dimensional (1d) Li0.9Mo6O17 display both agreement with and departures from the one-band Tomonaga-Luttinger model. We show that the departures can be understood by…

In the light of recent experimental and theoretical data, we go back to the studies tackled in previous publications [1] and develop some of their consequences. Some of their main aspects will be studied in further detail. Yet this text…

In this paper we study {\em terminal embeddings}, in which one is given a finite metric $(X,d_X)$ (or a graph $G=(V,E)$) and a subset $K \subseteq X$ of its points are designated as {\em terminals}. The objective is to embed the metric into…