- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 02:03:30
20
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=34&iss=3&update_since=2024-03-29
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
34
2018
3
Uniqueness for discrete Schrödinger evolutions
Philippe
Jaming
Université de Bordeaux, Talence, France
Yurii
Lyubarskii
The Norwegian University of Science and Technology, Trondheim, Norway
Eugenia
Malinnikova
Norwegian University of Science and Technology, Trondheim, Norway
Karl-Mikael
Perfekt
University of Reading, UK
Discrete Schrödinger equation, unique continuation, uncertainty principle
We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schr¨odinger operator, as well as for operators with compactly supported time-independent potentials, a sharp analog of the Hardy uncertainty principle is obtained, using an argument based on the theory of entire functions. Logarithmic convexity of weighted norms is employed in the case of general bounded potentials.
Potential theory
Difference and functional equations
Quantum theory
949
966
10.4171/RMI/1011
http://www.ems-ph.org/doi/10.4171/RMI/1011
8
27
2018
Local monomialization of a system of first integrals of Darboux type
André
Belotto da Silva
Université de Toulouse III Paul Sabatier, Toulouse, France
First integrals, monomialization, reduction of singularities, singular foliations
Given a real- or complex-analytic singular foliation $\theta$ with $n$ first integrals of meromorphic or Darboux type $(f_1,\dots,f_n)$, we prove that there exists a local monomialization of the first integrals. In particular, if $\theta$ is generated by the $n$ first integrals, we prove the existence of a local reduction of singularities of $\theta$ to monomial singularities.
Several complex variables and analytic spaces
Ordinary differential equations
967
1000
10.4171/RMI/1012
http://www.ems-ph.org/doi/10.4171/RMI/1012
8
27
2018
Critical points of non-regular integral functionals
Lucio
Boccardo
Università di Roma La Sapienza, Italy
Benedetta
Pellacci
Università degli Studi della Campania "Luigi Vanvitelli", Caserta, Italy
Non-smooth critical point theory, quasi-linear Schrödinger equations, quadratic growth in the gradient
We prove the existence of a bounded positive critical point for a class of functionals such as $$J(v)=\frac12\int_o [a(x)+b(x)|v|^{\gamma}]\, |\nabla v|^{2}-\int_o |v|^{p}$$ for $\Omega$ a bounded open set in $\mathbb R^{N}$, $N>2$,$\gamma+2< p < 2N/(N-2)$, $\gamma>0$, $\gamma\neq 1$ and $a(x),\,b(x)$ measurable function satisfying $0
Partial differential equations
Ordinary differential equations
1001
1020
10.4171/RMI/1013
http://www.ems-ph.org/doi/10.4171/RMI/1013
8
27
2018
Intertwinings and generalized Brascamp–Lieb inequalities
Marc
Arnaudon
Université de Bordeaux I, Talence, France
Michel
Bonnefont
Université de Bordeaux I, Talence, France
Aldéric
Joulin
Université de Toulouse, France
Intertwining, diffusion operator on vector fields, spectral gap, Brascamp–Lieb type inequalities, log-concave probability measure
We continue our investigation of the intertwining relations for Markov semigroups and extend our previous results to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp–Lieb type for log-concave distributions and beyond. Our results are illustrated by some classical and less classical examples.
Probability theory and stochastic processes
Dynamical systems and ergodic theory
Difference and functional equations
Operator theory
1021
1054
10.4171/RMI/1014
http://www.ems-ph.org/doi/10.4171/RMI/1014
8
27
2018
Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces
Juhani
Koivisto
University of Southern Denmark, Odense, Denmark
Controlled coarse homology, Sobolev inequalities
We give a Sobolev inequality characterisation for the vanishing of the fundamental class in the controlled coarse homology of Nowak and Špakula for quasiconvex uniform spaces that support a local weak (1, 1)-Poincaré inequality. Among the applications, we consider visual Gromov hyperbolic spaces.
Differential geometry
Functions of a complex variable
Global analysis, analysis on manifolds
1055
1070
10.4171/RMI/1015
http://www.ems-ph.org/doi/10.4171/RMI/1015
8
27
2018
$L^p$-bounds on spectral clusters associated to polygonal domains
Matthew
Blair
University of New Mexico, Albuquerque, USA
G. Austin
Ford
AltSchool, San Francisco, USA
Jeremy
Marzuola
University of North Carolina at Chapel Hill, USA
Spectral clusters, polygons, conic singularities
We look at the $L^p$ bounds on eigenfunctions for polygonal domains (or more generally Euclidean surfaces with conic singularities) by analysis of the wave operator on the flat Euclidean cone $C(\mathbb{S}^1_\rho) {\stackrel{\mathrm{def}}{=}} \mathbb{R}_+ \times \left(\mathbb{R} \big/ 2\pi\rho \mathbb{Z}\right)$ of radius $\rho > 0$ equipped with the metric h$(r,\theta) = \mathrm d r^2 + r^2 \, \mathrm d\theta^2$. Using explicit oscillatory integrals and relying on the fundamental solution to the wave equation in geometric regions related to flat wave propagation and diffraction by the cone point, we can prove spectral cluster estimates equivalent to those in works on smooth Riemannian manifolds.
Global analysis, analysis on manifolds
1071
1091
10.4171/RMI/1016
http://www.ems-ph.org/doi/10.4171/RMI/1016
8
27
2018
Multiplicative energy of polynomial images of intervals modulo $q$
Kyle
Castro
University of California, Riverside, USA
Mei-Chu
Chang
University of California, Riverside, USA
Character sums, polynomial images, subgroups of finite fields
Given a smooth integer $q$, we use existing upper bounds for character sums to find a lower bound for the size of a multiplicative subgroup of the integers modulo $q$ which contains the image of an interval of consecutive integers $I \subset \mathbb{Z}_q$ under a polynomial $f \in \mathbb{Z}[X]$.
Number theory
1093
1101
10.4171/RMI/1017
http://www.ems-ph.org/doi/10.4171/RMI/1017
8
27
2018
Lower bounds for codimension-1 measure in metric manifolds
Kyle
Kinneberg
National Security Agency, Fort Meade, USA
Hausdorff measure, isoperimetric inequality, linearly locally contractible metric manifold
We establish Euclidean-type lower bounds for the codimen\-sion-1 Hausdorff measure of sets that separate points in doubling and linearly locally contractible metric manifolds. This gives a quantitative topological isoperimetric inequality in the setting of metric manifolds, in the sense that lower bounds for the codimension-1 measure of a set depend not on some notion of filling or volume but rather on in-radii of complementary components. As a consequence, we show that balls in a closed, connected, doubling, and linearly locally contractible metric $n$-manifold $(M,d)$ with radius $0 < r \leq \mathrm {diam}(M)$ have $n$-dimensional Hausdorff measure at least~$c \cdot r^n$, where $c>0$ depends only on $n$ and on the doubling and linear local contractibility constants.
Measure and integration
Functions of a complex variable
1103
1118
10.4171/RMI/1018
http://www.ems-ph.org/doi/10.4171/RMI/1018
8
27
2018
A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions
Camillo
De Lellis
Universität Zürich, Switzerland
Dominik
Inauen
Universität Zürich, Switzerland
László
Székelyhidi Jr.
Universität Leipzig, Germany
Isometric embedding, convex integration, Nash–Kuiper
We prove that, given a $C^2$ Riemannian metric $g$ on the 2-dimensional disk $D_2$, any short $C^1$ immersion of $(D_2,g)$ into $\mathbb R^3$ can be uniformly approximated with $C^{1,\alpha}$ isometric immersions for any $\alpha < \frac{1}{5}$. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.
Manifolds and cell complexes
Differential geometry
Global analysis, analysis on manifolds
1119
1152
10.4171/RMI/1019
http://www.ems-ph.org/doi/10.4171/RMI/1019
8
27
2018
On zeros of analytic functions satisfying non-radial growth conditions
Alexander
Borichev
Aix Marseille Université, Marseille, France
Leonid
Golinskii
Institute for Low Temperature Physics, Kharkov, Ukraine
Stanislav
Kupin
Université de Bordeaux I, Talence, France
Zeros of analytic functions, generalized Blaschke condition, Jensen-type formulae
Extending the results of Borichev–Golinskii–Kupin (2009), we obtain refined Blaschke-type necessary conditions on the zero distribution of analytic functions on the unit disk and on the complex plane with a cut along the positive semi-axis satisfying some non-radial growth restrictions.
Functions of a complex variable
1153
1176
10.4171/RMI/1020
http://www.ems-ph.org/doi/10.4171/RMI/1020
8
27
2018
New bounds for bilinear Calderón–Zygmund operators and applications
Wendolín
Damián
Universidad de Sevilla, Spain
Mahdi
Hormozi
University of Gothenburg and Chalmers University of Technology, Göteborg, Sweden
Kangwei
Li
BCAM - Basque Center for Applied Mathematics, Bilbao, Spain
Domination theorem, Dini condition, multilinear Calderón–Zygmund operators, commutators, square functions, Fourier multipliers
In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini-continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_{\infty}$ constants inspired in the Fujii–Wilson and Hruscev classical constants. These estimates have many new applications including mixed bounds for multilinear Calderón–Zygmund operators and their commutators with BMO functions, square functions and multilinear Fourier multipliers.
Fourier analysis
1177
1210
10.4171/RMI/1021
http://www.ems-ph.org/doi/10.4171/RMI/1021
8
27
2018
Connectivity of Julia sets of Newton maps: a unified approach
Krzysztof
Barański
University of Warsaw, Poland
Núria
Fagella
Universitat de Barcelona, Spain
Xavier
Jarque
Universitat de Barcelona, Spain
Bogusława
Karpińska
Warsaw University of Technology, Poland
Newton’s method, root-finding algorithm, iteration, Julia set
In this paper we present a unified proof of the fact that the Julia set of Newton’s method applied to a holomorphic function on the complex plane (a polynomial of degree larger than 1 or a transcendental entire function) is connected. The result was recently completed by the authors’ previous work, as a consequence of a more general theorem whose proof spreads among many papers, which consider separately a number of particular cases for rational and transcendental maps, and use a variety of techniques. In this note we present a unified, direct and reasonably self-contained proof which works in all situations alike.
Functions of a complex variable
Dynamical systems and ergodic theory
1211
1228
10.4171/RMI/1022
http://www.ems-ph.org/doi/10.4171/RMI/1022
8
27
2018
A new strategy for resolution of singularities in the monomial case in positive characteristic
Hiraku
Kawanoue
Kyoto University, Japan
Kenji
Matsuki
Purdue University, West Lafayette, USA
Resolution of singularities, idealistic filtration program
According to our approach for resolution of singularities in positive characteristic (called the idealistic filtration program, IFP for short), the algorithm is divided into the following two steps: Step 1. Reduction of the general case to the monomial case. Step 2. Solution in the monomial case. While we have established Step 1 in arbitrary dimension, Step 2 becomes very subtle and difficult in positive characteristic. This is in clear contrast to the classical setting in characteristic zero, where the solution in the monomial case is quite easy. In dimension 3, we provided an invariant, inspired by the work of Benito–Villamayor, which establishes Step 2. In this paper, we propose a new strategy to approach Step 2, and provide a different invariant in dimension 3 based upon this strategy. The new invariant increases from time to time (the well-known Moh–Hauser jumpingphenomenon), while it is then shown to eventually decrease. Since the old invariant strictly decreases after each transformation, this may look like a step backward rather than forward. However, the construction of the new invariant is more faithful to the original philosophy of Villamayor, and we believe that the new strategy has a better fighting chance in higher dimensions.
Algebraic geometry
1229
1276
10.4171/RMI/1023
http://www.ems-ph.org/doi/10.4171/RMI/1023
8
27
2018
Boundedness of spectral multipliers for Schrödinger operators on open sets
Tsukasa
Iwabuchi
Tohoku University, Sendai, Japan
Tokio
Matsuyama
Chuo University, Tokyo, Japan
Koichi
Taniguchi
Chuo University, Tokyo, Japan
Schrödinger operators, functional calculus, Kato class
Let $H_V$ be a self-adjoint extension of the Schrödinger operator $-\Delta+V(x)$ with the Dirichlet boundary condition on an arbitrary open set~$\Omega$ of~$\mathbb R^d$, where $d \ge 1$ and the negative part of potential $V$ belongs to the Kato class on $\Omega$. The purpose of this paper is to prove $L^p$-$L^q$-estimates and gradient estimates for an operator $\varphi(H_V)$, where $\varphi$ is an arbitrary rapidly decreasing function on $\mathbb{R}$, and $\varphi(H_V)$ is defined via the spectral theorem.
Operator theory
Real functions
1277
1322
10.4171/RMI/1024
http://www.ems-ph.org/doi/10.4171/RMI/1024
8
27
2018
The Dirichlet problem for $p$-harmonic functions with respect to arbitrary compactifications
Anders
Björn
Linköping University, Sweden
Jana
Björn
Linköping University, Sweden
Tomas
Sjödin
Linköping University, Sweden
Dirichlet problem, harmonizable, invariance, metric space, nonlinear potential theory, Perron solution, $p$-harmonic function, $Q$-compactification, quasi-continuous, resolutive, Wiener solution
We study the Dirichlet problem for $p$-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev–Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)–Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)–Perron solutions, partly using $Q$-compactifications.
Potential theory
Functions of a complex variable
Partial differential equations
Calculus of variations and optimal control; optimization
1323
1360
10.4171/RMI/1025
http://www.ems-ph.org/doi/10.4171/RMI/1025
8
27
2018
Dislocations of arbitrary topology in Coulomb eigenfunctions
Alberto
Enciso
Consejo Superior de Investigaciones Científicas, Madrid, Spain
David
Hartley
Consejo Superior de Investigaciones Científicas, Madrid, Spain
Daniel
Peralta-Salas
Consejo Superior de Investigaciones Científicas, Madrid, Spain
Coulomb potential, nodal sets, knots
For any finite link $L$ in $\mathbb R^3$ we prove the existence of a complex-valued eigenfunction of the Coulomb Hamiltonian such that its nodal set contains a union of connected components diffeomorphic to $L$. This problem goes back to Berry, who constructed such eigenfunctions in the case where $L$ is the trefoil knot or the Hopf link and asked the question about the general result.
Partial differential equations
1361
1371
10.4171/RMI/1026
http://www.ems-ph.org/doi/10.4171/RMI/1026
8
27
2018
Explicit local multiplicative convolution of $\ell$-adic sheaves
Antonio
Rojas-León
Universidad de Sevilla, Spain
$/ell$-adic cohomology, convolution, Galois representations of local fields
We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two $\ell$-adic sheaves on the torus $\mathbb G_m$ over the algebraic closure of a finite field in terms of the local monodromies of the factors. As a particular case, we recover Fu's formulas for the local Fourier transform.
Algebraic geometry
Number theory
1373
1386
10.4171/RMI/1027
http://www.ems-ph.org/doi/10.4171/RMI/1027
8
27
2018
Structure of tangencies to distributions via the implicit function theorem
Silvano
Delladio
Università di Trento, Povo (Trento), Italy
Tangency set of a submanifold with respect to a distribution, applications of the implicit function theorem, multilinear algebra methods in real analysis
We investigate the structure and the dimension of the tangency set to a $C^1$ smooth distribution of $n$-dimensional vector subspaces of $\mathbb R^{n+m}$, by an argument based on the implicit function theorem.
Measure and integration
Linear and multilinear algebra; matrix theory
Operator theory
1387
1400
10.4171/RMI/1028
http://www.ems-ph.org/doi/10.4171/RMI/1028
8
27
2018
Sparse domination on non-homogeneous spaces with an application to $A_p$ weights
Alexander
Volberg
Michigan State University, East Lansing, USA
Pavel
Zorin-Kranich
Universität Bonn, Germany
Calderón–Zygmund operators, non-doubling measures, sparse operators
We extend Lerner's recent approach to sparse domination of Calderón–Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem, different from the one obtained recently by Conde-Alonso and Parcet, yields a weighted estimate with the sharp power max$(1,1/(p-1))$ of the $A_{p}$ characteristic of the weight.
Fourier analysis
General
1401
1414
10.4171/RMI/1029
http://www.ems-ph.org/doi/10.4171/RMI/1029
8
27
2018
Sparse domination on non-homogeneous spaces with an application to $A_p$ weights
Eva
Gallardo-Gutiérrez
Universidad Complutense de Madrid, Spain and Instituto de Ciencias Matemáticas, Madrid, Spain
Jonathan
Partington
University of Leeds, UK
2-isometries, right-shift semigroups, Dirichlet space
In the context of a theorem of Richter, we establish a similarity between $C_0$-semigroups of analytic $2$-isometries $\{T(t)\}_{t\geq0}$ acting on a Hilbert space $\mathcal H$ and the multiplication operator semigroup $\{M_{\phi_t}\}_{t\geq 0}$ induced by $\phi_t(s)=\mathrm {exp}(-st)$ for $s$ in the right-half plane $\mathbb{C}_+$ acting boundedly on weighted Dirichlet spaces on $\mathbb{C}_+$. As a consequence, we derive a connection with the right shift semigroup $\{S_t\}_{t\geq 0}$ given by $$S_tf(x)=\left \{ \begin{array}{ll} 0 & \mbox { if }0\leq x\leq t, \\ f(x-t)& \mbox { if } x>t, \end{array} \right .$$ acting on a weighted Lebesgue space on the half line $\mathbb{R}_+$ and address some applications regarding the study of the invariant subspaces\linebreak of $C_0$-semigroups of analytic 2-isometries.
Operator theory
1415
1425
10.4171/RMI/1030
http://www.ems-ph.org/doi/10.4171/RMI/1030
8
27
2018