Published volumes
19521968 Revista de la Unión Matemática Argentina y de la Asociación Física Argentina
19441951 Revista de la Unión Matemática Argentina; órgano de la Asociación Física Argentina
19361944

Online first articles
Articles are posted here individually soon after proof is returned from
authors, before the corresponding journal issue is completed. All
articles are in their final form, including issue number and pagination.
Currently this page contains articles for:
Vol. 63, no. 2 (2022)
Blowup of positiveinitialenergy solutions for nonlinearly damped semilinear wave equations.
Mohamed Amine Kerker
We consider a class of semilinear wave equations with both strongly and
nonlinear weakly damped terms,
\[
u_{tt}\Delta u\omega\Delta u_t+\mu\vert u_t\vert^{m2}u_t=\vert u\vert^{p2}u,
\]
associated with initial and Dirichlet boundary conditions. Under certain
conditions, we show that any solution with arbitrarily high positive initial
energy blows up in finite time if $m < p$. Furthermore, we obtain a lower bound
for the blowup time.

293–303 
Binomial edge ideals of cographs.
Thomas Kahle and Jonas Krüsemann
We determine the Castelnuovo–Mumford regularity of binomial edge ideals of
complementreducible graphs (cographs). For cographs with $n$ vertices the
maximum regularity grows as $2n/3$. We also bound the regularity by
graphtheoretic invariants and construct a family of counterexamples to
a conjecture of Hibi and Matsuda.

305–316 
A compact
manifold with infinitedimensional coinvariant cohomology.
Mehdi Nabil
Let $M$ be a smooth manifold. When $\Gamma$ is a group acting on $M$ by
diffeomorphisms, one can define the $\Gamma$coinvariant cohomology of $M$
to be the cohomology of the complex
$\Omega_c(M)_\Gamma=\operatorname{span}\{\omega\gamma^*\omega :
\omega\in\Omega_c(M),\,\gamma\in\Gamma\}$. For a Lie algebra $\mathcal{G}$
acting on the manifold $M$, one defines the cohomology of
$\mathcal{G}$divergence forms to be the cohomology of the complex
$\mathcal{C}_{\mathcal{G}}(M)=\operatorname{span}\{L_X\omega :
\omega\in\Omega_c(M),\,X\in\mathcal{G}\}$. In this short paper we present
a situation where these two cohomologies are infinite dimensional on a
compact manifold.

317–325 
Conformal vector fields on statistical manifolds.
Leila Samereh and Esmaeil Peyghan
Introducing the conformal vector fields on a statistical manifold, we present
necessary and sufficient conditions for a vector field on a statistical
manifold to be conformal. After presenting some examples, we classify the
conformal vector fields on two famous statistical manifolds. Considering
three statistical structures on the tangent bundle of a statistical
manifold, we study the conditions under which the complete and
horizontal lifts of a vector field can be conformal on these structures.

327–351 
The isometry
groups of Lorentzian threedimensional unimodular simply connected Lie groups.
Mohamed Boucetta and Abdelmounaim Chakkar
We determine the isometry groups of all threedimensional, connected, simply
connected and unimodular Lie groups endowed with a leftinvariant
Lorentzian metric.

353–378 
On the
differential and Volterratype integral operators on Focktype spaces.
Tesfa Mengestie
The differential operator fails to admit some basic structures including
continuity when it acts on the classical Fock spaces or weighted Fock
spaces, where the weight functions grow faster than the classical Gaussian
weight function. The same conclusion also holds in some weighted Fock
spaces including the Fock–Sobolev spaces, where the weight functions grow
more slowly than the Gaussian function. We consider modulating the classical
weight function and identify Focktype spaces where the operator admits the
basic structures. We also describe some properties of Volterratype
integral operators on these spaces using the notions of order and type of
entire functions. The modulation operation supplies richer structures for
both the differential and integral operators in contrast to the classical
setting.

379–395 
A note on the
density of the partial regularity result in the class of
viscosity solutions.
Disson dos Prazeres, Edgard A. Pimentel, and Giane C. Rampasso
We establish the density of the partial regularity result in the class of
continuous viscosity solutions. Given a fully nonlinear equation, we prove
the existence of a sequence entitled to the partial regularity result,
approximating its solutions. Distinct conditions on the operator driving
the equation lead to density in different topologies. Our findings include
applications to nonhomogeneous problems, with variablecoefficient models.

397–411 
Monster graphs
are determined by their Laplacian spectra.
Ali Zeydi Abdian, Ali Reza Ashrafi, Lowell W.
Beineke, Mohammad Reza Oboudi, and Gholam Hossein FathTabar
A graph $G$ is determined by its Laplacian spectrum (DLS) if every graph with
the same Laplacian spectrum is isomorphic to $G$. A multifan graph is a
graph of the form $(P_{n_1}\cup P_{n_2}\cup \cdots \cup
P_{n_k})\bigtriangledown K_1$, where $K_1$ denotes the complete graph of
size 1, $P_{n_1}\cup P_{n_2}\cup \cdots \cup P_{n_k}$ is the disjoint union
of paths $P_{n_i}$, $n_i\geq 1$ and $1 \leq i \leq k$; and a starlike tree
is a tree with exactly one vertex of degree greater than 2. If a
multifan graph and a starlike tree are joined by identifying their
vertices of degree more than 2, then the resulting graph is called a
monster graph. In some earlier works, it was shown that all multifan and
pathfriendship graphs are DLS. The aim of this paper is to generalize
these facts by proving that all monster graphs are DLS.

413–424 
Sharp bounds for
fractional type operators with $L^{\alpha,s}$Hörmander conditions.
Gonzalo H. IbañezFirnkorn, María Silvina Riveros,
and Raúl E. Vidal
We provide the sharp bound for a fractional type operator given by a kernel
satisfying the $L^{\alpha,s}$Hörmander condition and certain fractional
size condition, $0 < \alpha < n$ and $1 < s\leq \infty$. In order to prove
this result we use a new appropriate sparse domination. Examples of these
operators include the fractional rough operators. For the case $s=\infty$
we recover the sharp bound of the fractional integral, $I_{\alpha}$, proved
by Lacey et al.
[J. Functional Anal. 259 (2010), no. 5, 1073–1097].

425–442 
The isolation of
the first eigenvalue for a Dirichlet eigenvalue problem involving
the Finsler $p$Laplacian and a nonlocal term.
Andrei Grecu
We analyse the isolation of the first eigenvalue for an eigenvalue problem
involving the Finsler $p$Laplace operator and a nonlocal term on a bounded
domain subject to the homogeneous Dirichlet boundary condition.

443–453 
Vol. 64, no. 2 (2022)
Special volume: Mathematical Congress of the Americas 2021
Editors:
Guillermo Cortiñas (managing editor, Universidad de Buenos Aires);
Renato Iturriaga (CIMAT, Guanajuato, Mexico);
Andrea Nahmod (University of Massachusetts, Amherst, USA);
Jimmy Petean (CIMAT, Guanajuato, Mexico);
Arturo Pianzola (University of Alberta, Canada and Universidad CAECE, Argentina);
Cecilia Salgado (University of Groningen, Netherlands and Universidade Federal do Rio de Janeiro, Brazil);
Soledad Torres (CIMFAVINGEMAT, Universidad de Valparaíso, Chile);
Bernardo Uribe (Universidad del Norte, Colombia);
Steven Weintraub (Lehigh University, Bethlehem, USA).
Preface.
Guillermo Cortiñas

Univariate
rational sums of squares.
Teresa Krick, Bernard Mourrain, and Agnes Szanto
Given rational univariate polynomials $f$ and $g$ such that $\gcd (f,g)$ and
$f/\gcd(f,g)$ are relatively prime, we show that $g$ is nonnegative at all
the real roots of $f$ if and only if $g$ is a sum of squares of rational
polynomials modulo $f$. We complete our study by exhibiting an algorithm
that produces a certificate that a polynomial $g$ is nonnegative at the
real roots of a nonzero polynomial $f$ when the above assumption is
satisfied.

215–237 
A note on Bernstein–Sato ideals.
Josep Àlvarez Montaner
We define the Bernstein–Sato ideal associated to a tuple of ideals and we
relate it to the jumping points of the corresponding mixed multiplier ideals.

239–246 
On
essential selfadjointness of singular
Sturm–Liouville operators.
S. Blake Allan, Fritz Gesztesy, and Alexander Sakhnovich
Considering singular Sturm–Liouville differential expressions of the type
\[
\tau_{\alpha} = (d/dx)x^{\alpha}(d/dx) + q(x),
\quad x \in (0,b), \, \alpha \in \mathbb{R},
\]
we employ some Sturm comparisontype results in the spirit of Kurss to derive
criteria for $\tau_{\alpha}$ to be in the limitpoint and limitcircle case
at $x=0$. More precisely, if $\alpha \in \mathbb{R}$ and, for $0 < x$
sufficiently small,
\[
q(x) \geq [(3/4)(\alpha/2)]x^{\alpha2},
\]
or, if $\alpha\in (\infty,2)$ and there exist $N\in\mathbb{N}$ and $\varepsilon>0$
such that, for $0 < x$ sufficiently small,
\begin{align*}
& q(x)\geq[(3/4)(\alpha/2)]x^{\alpha2}  (1/2) (2  \alpha) x^{\alpha2}
\sum_{j=1}^{N}\prod_{\ell=1}^{j}[\ln_{\ell}(x)]^{1}
\\
& \quad\quad\quad +[(3/4)+\varepsilon] x^{\alpha2}[\ln_{1}(x)]^{2},
\end{align*}
then $\tau_{\alpha}$ is nonoscillatory and in the limitpoint case at $x=0$.
Here iterated logarithms for $0 < x$ sufficiently small are of the form
\[
\ln_1(x) = \ln(x) = \ln(1/x),
\qquad
\ln_{j+1}(x) = \ln(\ln_j(x)), \quad j \in \mathbb{N}.
\]
Analogous results are derived for $\tau_{\alpha}$ to be in the limitcircle
case at $x=0$.
We also discuss a multidimensional application to partial differential
expressions of the type
\[
 \operatorname{div} x^{\alpha} \nabla + q(x),
\quad \alpha \in \mathbb{R}, \, x \in B_n(0;R) \backslash \{0\},
\]
with $B_n(0;R)$ the open ball in $\mathbb{R}^n$, $n\in \mathbb{N}$, $n \geq 2$,
centered at $x=0$ of radius $R \in (0, \infty)$.

247–269 
Inequivalent representations of the dual space.
Tepper L. Gill, Douglas Mupasiri, and Erdal Gül
We show that there exist inequivalent representations of the dual space of
$\mathbb{C}[0,1]$ and of $L_p[\mathbb{R}^n]$ for $p \in [1,\infty)$. We
also show how these inequivalent representations reveal new and important
results for both the operator and the geometric structure of these spaces.
For example, if $\mathcal{A}$ is a proper closed subspace of
$\mathbb{C}[0,1]$, there always exists a closed subspace $\mathcal{A}^\bot$
(with the same definition as for $L_2[0,1]$) such that $\mathcal{A} \cap
\mathcal{A}^\bot = \{0\}$ and $\mathcal{A} \oplus \mathcal{A}^\bot =
\mathbb{C}[0,1]$. Thus, the geometry of $\mathbb{C}[0,1]$ can be viewed
from a completely new perspective. At the operator level, we prove that
every bounded linear operator $A$ on $\mathbb{C}[0,1]$ has a uniquely
defined adjoint $A^*$ defined on $\mathbb{C}[0,1]$, and both can be
extended to bounded linear operators on $L_2[0,1]$. This leads to a polar
decomposition and a spectral theorem for operators on the space. The same
results also apply to $L_p[\mathbb{R}^n]$. Another unexpected result is a
proof of the Baire one approximation property (every closed densely defined
linear operator on $\mathbb{C}[0,1]$ is the limit of a sequence of bounded
linear operators). A fundamental implication of this paper is that the use
of inequivalent representations of the dual space is a powerful new tool
for functional analysis.

271–280 
