Related papers: Frame bound, spectral gap and Plus space

We develop a general framework for spectral gap inequalities for Gibbs measures on infinite dimensional spin spaces over nilpotent Lie groups in terms of weak U-bounds and weak single-site spectral gap inequalities. We then provide…

The vertex-weighted Laplacian naturally extends the combinatorial Laplacian for simplicial complexes. Inspired by Lew's foundational techniques for vertex-weighted Laplacians, we present a comprehensive spectral analysis of this operator.…

In this article, we derive two spectral gap bounds for the reduced Laplacian of a general simplicial complex. Our two bounds are proven by comparing a simplicial complex in two different ways with a larger complex and with the corresponding…

For smooth bounded domains in $\mathbb{R}$, we prove upper and lower $L^2$ bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary data in a spectral window. The bounds are tight in the sense…

In this note we propose a min-max theory for embedded hypersurfaces with a fixed boundary and apply it to prove several theorems about the existence of embedded minimal hypersurfaces with a given boundary. A simpler variant of these…

We obtain a new bound connecting the first non--trivial eigenvalue of the Laplace operator of a graph and the diameter of the graph, which is effective for graphs with small diameter or for graphs, having the number of maximal paths…

We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. We then prove that pseudo-dual frames…

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a…

In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the…

We establish a new spectral inequality for the quantified estimation of the $H^s$-norm, $s\ge 0$ of a finite linear combination of eigenfunctions in a domain in terms of its $H^s$-norm in a strictly open subset of the whole domain. The…

In this paper, we present a sharp upper and lower bounds for the signless Laplacian spectral radius of graphs in terms of clique number. Moreover, the extremal graphs which attain the upper and lower bounds are characterized. In addition,…

We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with $C^2$ boundaries. We show that for an $n$-dimensional geometry, the spectral gap is bounded above by $(n-1)^2/4$, which we…

We improve Frank-Sabin's work concerning the spectral cluster bounds for orthonormal systems at $p=\infty$, on the flat torus and spaces of nonpositive sectional curvature, by shrinking the spectral band from $[\lambda^{2},…

We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an application to the initial boundary value problem for a…

Theoretical limits and physical bounds across many areas of science, mathematics, and technology -- including Shannon's information-capacity limits, Bennett and Landauer's thermodynamic limits on computation, and G\"odel's incompleteness…

We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \emph{$\mathcal O(n)$-models} with mean-field interaction and magnetic field, below and at the critical temperature on the number $N$ of…

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…

We study sparsity and spectral properties of dual frames of a given finite frame. We show that any finite frame has a dual with no more than $n^2$ non-vanishing entries, where $n$ denotes the ambient dimension, and that for most frames no…

In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare…

We construct a uniformly expanding map of the interval, preserving Lebesgue measure, such that the corresponding transfer operator admits a spectral gap on the space of Lipschitz functions, but does not act continuously on the space of…