Related papers: On the chain structure in the de Branges spaces

I consider flat slices of moduli spaces where the $(-\nabla \log T)$-vectors of particle-towers and branes are constant, and I show that the Emergent String Conjecture constrains these vectors to reside on lattices. In asymptotic limits,…

Let $(X,(p_j))$ be a Fr\'echet space with a Schauder basis and without continuous norm, where $(p_j)$ is an increasing sequence of seminorms inducing the topology of $X$. We show that $X$ satisfies the Invariant Subspace Property if and…

A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…

We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schroedinger equations on the disc of the plane $\R^2$. We also prove an estimate giving some intuition to what may happen in 3…

We consider the propagation of Type I open superstrings on orbifolds with four non-compact dimensions and $N=1$ supersymmetry. In this paper, we concentrate on a non-trivial Z_2xZ_2 example. We show that consistency conditions, arising from…

We establish discrete Ingham type and Haraux type inequalities for exponential sums satisfying a weakened gap condition. They enable us to obtain discrete simultaneous observability theorems for systems of vibrating strings or beams.

We provide a broad class of counterexamples to a conjecture of L. de Branges concerning the superfluity of the continuity property in the axiomatic description of de Branges spaces.

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is…

Cauchy-de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of…

In this paper, we study the descriptive complexity of some inevitable classes of Banach spaces. Precisely, as shown in [Go], every Banach space either contains a hereditarily indecomposable subspace or an unconditional basis, and, as shown…

We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational…

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we…

In this paper, we first explore exponential stability by using Monotonicity inequality and use this information to obtain the existence of Invariant measure for linear Stochastic PDEs with potential in the space of tempered distributions.…

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

We investigate the following questions: Given a measure $\mu_\Lambda$ on configurations on a subset $\Lambda$ of a lattice $\mathbb{L}$, where a configuration is an element of $\Omega^\Lambda$ for some fixed set $\Omega$, does there exist a…

Let a finite set of points $\{\xi_1,...,\xi_k\}$ be chosen in a metric space $(X,d)$, and let the squared distance matrix $\mathfrak{D}=(\mathfrak{D}(\xi_i,\xi_j)^2)_{i,j=1}^{k}$ be constructed from them. We propose a geometric approach to…

On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends…

Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…