Related papers: On Tangential and Projectively Adjacent Approach R…

Recent works by Bot-Fadili-Nguyen (arXiv:2510.22715) and by Jang-Ryu (arXiv:2510.23513) resolve long-standing iterate convergence questions for accelerated (proximal) gradient methods. In particular, Bot-Fadili-Nguyen prove weak convergence…

We consider a Laurent series defined by infinite products $g_u(t) = \prod_{n=0}^\infty (1 + ut^{-2^n})$, where $u\in \mathbb{F}$ is a parameter and $\mathbb{F}$ is a field. We show that for all $u\in\mathbb{Q}\setminus\{-1,0,1\}$ the series…

We present a general framework for weak convergence to decorated L\'evy processes in enriched spaces of c\`adl\`ag functions for vector-valued processes arising in deterministic systems. Applications include uniformly expanding maps and…

The fundamental theorem of geometry of rectangular matrices describes the general form of bijective maps on the space of all $m\times n$ matrices over a division ring $\mathbb{D}$ which preserve adjacency in both directions. This result…

The purpose of this paper is to develop a Lie algebraic approach to obtain new proofs of important results of H.-C. Wang, Tits and Wolf-Wang-Ziller on compact complex homogeneous manifolds emphasizing only those that admit a transitive…

Let $f:\mathbb{D}\to\mathbb{C}$ be a bounded analytic function. A set $K\subset\mathbb{D}$ which contains the point $1$ in its boundary is called a convergence set for $f$ at $1$ if $f(z)$ converges to some value $\zeta$ as $z\to1$ with…

Convergence of diagonal Pad\'e approximants is studied for a class of functions which admit the integral representation $ {\mathfrak F}(\lambda)=r_1(\lambda)\int_{-1}^1\frac{td\sigma(t)}{t-\lambda}+r_2(\lambda), $ where $\sigma$ is a finite…

In 2004, de Mathan and Teuli\'e stated the $p$-adic Littlewood Conjecture ($p$-$LC$) in analogy with the classical Littlewood Conjecture. Given a field $\mathbb{K}$ and an irreducible polynomial $p(t)$ with coefficients in $\mathbb{K}$,…

There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of…

It is a classical theorem that if a function is integrable along the boundary of the unit circle, then the function is the nontangential limit of a holomorphic function on the open disc if and only if its Fourier coefficients for…

This paper combines two ingredients in order to get a rather surprising result on one of the most studied, elegant and powerful tools for solving convex feasibility problems, the method of alternating projections (MAP). Going back to names…

Let $M$ be an $m$-dimensional differentiable manifold with a nontrivial circle action ${\mathcal S}= {\lbrace S_t \rbrace}_{t \in\RR}, S_{t+1}=S_t$, preserving a smooth volume $\mu$. For any Liouville number $\a$ we construct a sequence of…

The paper describes relations between Liouville type theorems for solutions of a periodic elliptic equation (or a system) on an abelian cover of a compact Riemannian manifold and the structure of the dispersion relation for this equation at…

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out…

We associate to a perturbation $(f_t)$ of a (stably mixing) piecewise expanding unimodal map $f_0$ a two-variable fractional susceptibility function $\Psi_\phi(\eta, z)$, depending also on a bounded observable $\phi$. For fixed $\eta \in…

In this paper we establish several invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in $\mathbb C^N$ in the spirit of…

We discuss conformal manifolds for conformal field theories with boundaries or defects. Using conformal perturbation theory we derive constraints on coefficients appearing in the boundary operator product expansion and three-point functions…

In 1955, Lehto showed that, for every measurable function $\psi$ on the unit circle $\mathbb T,$ there is function $f$ holomorphic in the unit disc $\mathbb D,$ having $\psi$ as radial limit a.e. on $\mathbb T.$ We consider an analogous…

This note is a synthesis of my reflexions on some questions that have emerged during the MATRIX event "Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type" concerning the qualitative properties of solutions to some non local…