Micu, Sorin Pazoto, Ademir F.
Published in
Journal d'Analyse Mathématique

A family of Boussinesq systems was proposed by J. L. Bona, M. Chen, and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. Our work considers a class of these Boussinesq systems which couples two Benjamin-Bona-Mahony type equations posed on a bounded interval. We study the stabilizati...

Soave, Nicola Valdinoci, Enrico
Published in
Journal d'Analyse Mathématique

We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. We also study the extension of the result in bounded non-convex regions, as well as the radial symmetry of the solution when the set is as...

Dimitrov, Dimitar K. Oliveira, Willian D.
Published in
Journal d'Analyse Mathématique

We prove that the signs of the Maclaurin coefficients of a wide class of entire functions that belong to the Laguerre–Pólya class possess a regular behaviour.

Aleman, Alexandru Olsen, Jan-Fredrik Saksman, Eero
Published in
Journal d'Analyse Mathématique

We study the boundary behavior of functions in the Hardy spaces on the infinite-dimensional polydisc. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz- Zygmund type theorems for radial convergence of functions with Fourier spectrum supported on N0∞∪(−N0∞)\documentclass[12pt]{min...

Matsuyama, Tokio Ruzhansky, Michael
Published in
Journal d'Analyse Mathématique

This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space γη,L2s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} ...

Nicola, Fabio
Published in
Journal d'Analyse Mathématique

We consider the time slicing approximations of Feynman path integrals, constructed via piecewice classical paths. A detailed study of the convergence in the norm operator topology, in the space B(L2(ℝd)) of bounded operators on L2, and even in finer operator topologies, was carried on by D. Fujiwara in the case of smooth potentials with an at most ...

Christiansen, Jacob S.
Published in
Journal d'Analyse Mathématique

We introduce the Szegő class, Sz(E), for an arbitrary Parreau–Widom set E ⊂ ℝ and study the dynamics of its elements under the left shift. When the direct Cauchy theorem holds on ℂ\E, we show that to each J ∈ Sz(E) there is a unique element J′ in the isospectral torus, TE, so that the left-shifts of J are asymptotic to the orbit {J′m} on TE. Moreov...

Bergelson, Vitaly Kolesnik, Grigori Son, Younghwan
Published in
Journal d'Analyse Mathématique

Let H be a Hardy field (a field consisting of germs of real-valued functions at infinity that is closed under differentiation) and let f ∈ H be a subpolynomial function. Let P be the sequence of naturally ordered primes. We show that (f(n))n∈ℕ is uniformly distributed mod1 if and only if (f (p))p∈P is uniformly distributed mod 1. This result is the...

Papachristodoulos, C. Papadimitrakis, M.
Published in
Journal d'Analyse Mathématique

We construct functions in the disc algebra whose Fourier series are pointwise universal on countable and dense sets and their sets of divergence contain Gδ and dense sets and have Hausdorff dimension zero. We also see that some classes of closed sets of measure zero do not accept uniformly universal Fourier series, although all such sets accept div...

Foreman, Matthew Weiss, Benjamin
Published in
Journal d'Analyse Mathématique

This paper is the first of a series of papers culminating in the result that measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable. It addresses another classical problem: which abstract measure preserving systems are realizable as smooth diffeomorphisms of a compact manifold? The main result gives symbolic representations of...