Related papers: Shift-invariant sampling in two-sided small Fock s…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
We will study a certain synchronizing property of subshifts called $\lambda$-synchronization. The $\lambda$-synchronizing subshifts form a large class of irreducible subshifts containing irreducible sofic shifts. We prove that the…
We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This…
We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
We prove a contraction property of Fock type spaces $\mathcal{L}_{\alpha}^p$ of log-subharmonic functions in $\mathbb{R}^n$. To prove the result, we demonstrate a certain monotonic property of measures of the superlevel set of the function…
We propose a sequential topology on the space of sub-$\sigma$-algebras of a separable probability space $(\Omega,\mathcal{F},\mathbb{P})$ by linking conditional expectations on $L^{2}$ along sequences of sub-$\sigma$-algebras. The varying…
We describe a very simple method for `consistent sampling' that allows for sampling with replacement. The method extends previous approaches to consistent sampling, which assign a pseudorandom real number to each element, and sample those…
This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis in Paris. This line of research was initiated by a question of Haight and Weizs\"aker concerning almost everywhere convergence properties of series of…
It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
In this paper, we study the linear structure of sets $A \subset \mathbb{F}_2^n$ with doubling constant $\sigma(A)<2$, where $\sigma(A):=\frac{|A+A|}{|A|}$. In particular, we show that $A$ is contained in a small affine subspace. We also…
This paper is devoted to the $L^p(\mathbb R)$ theory of the fractional Fourier transform (FRFT) for $1\le p < 2$. In view of the special structure of the FRFT, we study FRFT properties of $L^1$ functions, via the introduction of a suitable…
We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the…
We present an accurate ab initio method of calculating isotope shifts and relativistic shifts in atomic spectra. We test the method on neutral carbon and three carbon ions. The relativistic shift of carbon lines may allow them to be…
Under different assumptions on the potential functions $b$ and $c$, we study the fractional equation $\left( I-\Delta \right)^{\alpha} u = \lambda b(x) |u|^{p-2}u+c(x)|u|^{q-2}u$ in $\mathbb{R}^N$. Our existence results are based on compact…
A compatible point-shift $F$ maps, in a translation invariant way, each point of a stationary point process $\Phi$ to some point of $\Phi$. It is fully determined by its associated point-map, $f$, which gives the image of the origin by $F$.…
Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call…
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…