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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

Volumen 50, número 1 (2009)
Roque Scarfiello (19162008).
Norberto Fava
PDF

iii 
A description of hereditary skew group algebras of
Dynkin and Euclidean type.
Olga Funes
PDF
In this work we study the skew group algebra $\Lambda[G]$
when $G$ is a finite group acting on $\Lambda$ whose order is
invertible in $\Lambda$. Here, we assume that $\Lambda$ is a
finitedimensional algebra over an algebraically closed field
$k$. The aim is to describe all possible actions of a finite
abelian group on an hereditary algebra of finite or tame
representation type, to give a description of the resulting
skew group algebra for each action and finally to determinate
their representation type.

122 
A compact trace theorem for domains with external
cusps.
Carlos Zuppa
PDF
This paper deals with the compact trace theorem in domains
$\Omega \subset \mathbb{R}^3$ with external cusps.
We show that if the power sharpness of the cusp is
bellow a critical exponent, then the trace operator
$\gamma : H^1 (\Omega) \rightarrow L^2 (\partial\Omega)$
exists and it is compact.

2329 
Simultaneous approximation by a new sequence of
SzãszBeta type operators.
Ali J. Mohammad and Amal K. Hassan
PDF
In this paper, we study some direct results in simultaneous ap
proximation for a new sequence of linear positive operators
$M_n(f(t); x)$ of
SzãszBeta type operators. First, we establish the basic pointwise convergence
theorem and then proceed to discuss the Voronovaskajatype asymptotic formula.
Finally, we obtain an error estimate in terms of modulus of continuity
of the function being approximated.

3140 
Amalgamation property in quasimodal algebras.
Sergio Arturo Celani
PDF
In this paper we will give suitable notions of Amalgamation and
Superamalgamation properties for the class of quasimodal algebras introduced
by the author in his paper QuasiModal algebras.

4146 
The subvariety of $Q$Heyting algebras
generated by chains.
Laura A. Rueda
PDF
The variety $\mathcal{QH}$ of Heyting algebras with a
quantifier [14] corresponds to the algebraic study of the modal
intuitionistic propositional calculus without the necessity
operator. This paper is concerned with the subvariety
$\mathcal{C}$ of $\mathcal{QH}$ generated by chains. We prove
that this subvariety is characterized within $\mathcal{QH}$ by
the equations $\nabla(x \wedge y) \approx \nabla x \wedge
\nabla y$ and $(x \rightarrow y) \vee (y \rightarrow x) \approx
1$. We investigate free objects in $\mathcal{C}$.

4759 
Approximation degree for generalized integral operators.
S. Jain and R. K. Gangwar
PDF
Very recently Jain et al. [4] proposed generalized
integrated Baskakov operators
$V_{n,\alpha} (f,x)$,
$\alpha > 0$ and estimated some approximation properties in
simultaneous approximation. In the present paper we establish
the rate of convergence of these operators and its Bezier
variant, for functions which have derivatives of bounded
variation.

6168 
Exponents of modular reductions of families of elliptic curves.
Igor E. Shparlinski
PDF
For some natural families of elliptic curves we show that “on average”
the exponent of the point group of their reductions modulo a prime $p$
grows as $p^{1+o(1)}$.

6974 
Exponential families of minimally noncoordinated graphs.
Francisco Soulignac and Gabriel Sueiro
PDF
A graph $G$ is coordinated if, for every induced
subgraph $H$ of $G$, the minimum number of colors
that can be assigned to the cliques of $H$ in such a way
that no two cliques with nonempty intersection receive the
same color is equal to the maximum number of cliques of
$H$ with a common vertex. In a previous work, coordinated
graphs were characterized by minimal forbidden induced
subgraphs within some classes of graphs. In this note, we
present families of minimally noncoordinated graphs whose
cardinality grows exponentially on the number of vertices and
edges. Furthermore, we describe some ideas to generate similar
families. Based on these results, it seems difficult to find a
general characterization of coordinated graphs by minimal
forbidden induced subgraphs.

7585 
Functional versions of the CaristiKirk theorem.
Mihai Turinici
PDF
Many functional versions of the CaristiKirk fixed point theorem
are nothing but logical equivalents of the result in question.

8797 
Hecke operators on cohomology.
Min Ho Lee
PDF
Hecke operators play an important role in the theory of automorphic forms,
and automorphic forms are closely linked to various cohomology
groups. This paper is mostly a survey of Hecke operators acting on certain
types of cohomology groups. The class of cohomology on which Hecke operators
are introduced includes the group cohomology of discrete subgroups of a
semisimple Lie group, the de Rham cohomology of locally symmetric spaces,
and the cohomology of symmetric spaces with coefficients in a system of local
groups. We construct canonical isomorphisms among such cohomology
groups and discuss the compatibility of the Hecke operators with respect to
those canonical isomorphisms.

99144 
Weak type (1, 1) of maximal operators on metric
measure spaces.
Marilina Carena
PDF
A discretization method for the study of the weak type (1, 1) for
the maximal of a sequence of convolution operators on $\mathbb{R}^n$ has been introduced
by Miguel de Guzmán and Teresa Carrillo, by replacing the integrable
functions by finite sums of Dirac deltas. Trying to extend the above mentioned
result to integral operators defined on metric measure spaces, a general setting
containing at once continuous, discrete and mixed contexts, a caveat comes
from the result in On restricted weak type (1, 1); the discrete case (Akcoglu
M.; Baxter J.; Bellow A.; Jones R., Israel J. Math. 124 (2001), 285297).
There a sequence of convolution operators in $\ell^1(\mathbb{Z})$ is constructed such that
the maximal operator is of restricted weak type (1, 1), or equivalently of weak
type (1, 1) over finite sums of Dirac deltas, but not of weak type (1, 1). The
purpose of this note is twofold. First we prove that, in a general metric
measure space with a measure that is absolutely continuous with respect to some
doubling measure, the weak type (1, 1) of the maximal operator associated to
a given sequence of integral operators is equivalent to the weak type (1, 1) over
linear combinations of Dirac deltas with positive integer coefficients. Second,
for the nonatomic case we obtain as a corollary that any of these weak type
properties is equivalent to the weak type (1, 1) over finite sums of Dirac deltas
supported at different points.

145159 
Formulas for the EulerMascheroni constant.
Pablo A. Panzone
PDF
We give several integral representations for the EulerMascheroni
constant using a combinatorial identity for
$\sum_{n=1}^N \frac{1}{(n+x)(n+y)}$.
The derivation of this combinatorial identity is done in an elemental way.

161164 
2008 / LVIII Reunión anual de Comunicaciones Científicas
de la Unión Matemática Argentina y XXXI Reunión de Educación Matemática.
PDF

165166 
Volumen 50, número 2 (2009)
Haar shifts, commutators, and Hankel operators.
Michael Lacey
PDF
Hankel operators lie at the junction of analytic and
realvariables. We will explore this junction, from the point
of view of Haar shifts and commutators.

113 
Atomic decompositions and operators on Hardy spaces.
Stefano Meda, Peter Sjögren and Maria Vallarino
PDF
This paper is essentially the second authors' lecture at the
CIMPAUNESCO Argentina School 2008, Real Analysis and its
Applications. It summarises large parts of the three authors'
paper [MSV]. Only one proof is given. In the setting of a
Euclidean space, we consider operators defined and uniformly
bounded on atoms of a Hardy space $H^p$. The
question discussed is whether such an operator must be bounded
on $H^p$. This leads to a study of the
difference between countable and finite atomic decompositions
in Hardy spaces.
[MSV] S. Meda, P. Sjögren and M. Vallarino, On the
$H^1$$L^1$ boundedness of operators,
Proc. Amer. Math. Soc. 136 (2008), 29212931.

1522 
Notes on the spaces of bilinear multipliers.
Oscar Blasco
PDF
A locally integrable function $m(\xi, \eta)$ defined on
$\mathbb{R}^n \times \mathbb{R}^n$ is said
to be a bilinear multiplier on $\mathbb{R}^n$ of type
$(p_1, p_2, p_3)$ if
$$
B_m(f,g)(x) = \int_{\mathbb{R}^n}\int_{\mathbb{R}^n}
\hat{f}(\xi) \hat{g}(\eta) m(\xi,\eta) e^{2\pi i\langle\xi+\eta, x\rangle} \, d\xi d\eta
$$
defines a bounded bilinear operator from
$L^{p_1}(\mathbb{R}^n) \times L^{p_2}(\mathbb{R}^n)$ to
$L^{p_3}(\mathbb{R}^n)$. The
study of the basic properties of such spaces is investigated
and several methods of constructing examples of bilinear
multipliers are provided. The special case where $m(\xi, \eta)
= M(\xi  \eta)$ for a
given $M$ defined on $\mathbb{R}^n$ is also addressed.

2337 
Transference of $L^p$boundedness between
harmonic analysis operators for Laguerre and Hermite settings.
Jorge J. Betancor
PDF
In this paper we discuss a transference method of $L^p$boundedness
properties for harmonic analysis operators in the Hermite setting to the corresponding
operators in the Laguerre context. As a byproduct of our procedure
we obtain new characterizations of certain classes of Banach spaces and Köethe
spaces.

3949 
Mixed weak type inequalities for onesided operators
and ergodic theorems.
F. J. MartínReyes
PDF
This paper is essentially the talk I addressed in the CIMPAUNESCO Argentina
School 2008. It is about mixed weak type inequalities and it is based
on a joint paper with S. Ombrosi:
Francisco J. MartínReyes and Sheldy J. Ombrosi, Mixed weak type
inequalities for onesided operators, Q. J. Math. 60 (2009),
no. 1, 6373.

5161 
Gelfand pairs related to groups of Heisenberg type.
Linda Saal
PDF
In this article we collect some known results concerning
(generalized) Gelfand pairs $(K, N)$, where $N$ is a group of Heisenberg
type and $K$ is a subgroup of automorphisms of $N$. We also
give new examples.

6374 
Harmonic analysis on Heisenberg nilmanifolds.
Sundaram Thangavelu
PDF
In these lectures we plan to present a survey of certain
aspects of harmonic analysis on a Heisenberg nilmanifold
$\Gamma\backslash \mathbb{H}^n$. Using WeilBrezinZak transform we obtain an
explicit decomposition of $L^2(\Gamma\backslash \mathbb{H}^n)$ into irreducible
subspaces invariant under the right regular representation of
the Heisenberg group. We then study the SegalBargmann
transform associated to the Laplacian on a nilmanifold and
characterise the image of $L^2(\Gamma\backslash \mathbb{H}^n)$ in terms of
twisted Bergman and Hermite Bergman spaces.

7593 
Entire solutions of the AllenCahn equation and
complete embedded minimal surfaces.
Manuel Del Pino, Michal Kowalczyk, and Juncheng Wei
PDF
We review some recent results on construction of entire solutions
to the classical semilinear elliptic equation
$\Delta u + u  u^3 = 0$ in $\mathbb{R}^N$.
In various cases, large dilations of an embedded, complete
minimal surface approximate the transition set of a solution
that connects the equilibria $\pm 1$. In particular, our
construction answers negatively a celebrated conjecture by
E. De Giorgi in dimensions $N \geq 9$.

95107 
Pointwise estimates for gradients of temperatures in
terms of maximal functions.
Hugo Aimar, Ivana Gómez, and Bibiana Iaffei
PDF
We give a detailed proof, in the case of one space dimension,
of a pointwise upper estimate for the space gradient of a temperature. The
operators involved are a onesided HardyLittlewood maximal in time and the
Calderón sharp maximal operator in space.

109118 
The growth of the $A_p$ constant on
classical estimates.
Carlos Pérez
PDF
We survey on some recent results concerning weak and strong
weighted $L^p$ estimates for CalderónZygmund operators with
sharp bounds when the weight satisfies the $A_1$
condition. These questions are related to a problem posed by
Muckenhoupt and Wheeden in the seventies.

119135 
A note on maximal operators associated with Hankel
multipliers.
Gustavo Garrigós and Andreas Seeger
PDF
Let $m$ have compact support in $(0, \infty)$.
For $1 < p < 2d/(d + 1)$, we give a
necessary and sufficient condition for the
$L^p_\mathrm{rad}(\mathbb{R}^d)$boundedness
of the maximal operator associated with the radial multiplier
$m(\xi)$. More generally we prove a similar result for
maximal operators associated with multipliers of modified
Hankel transforms. The result is obtained by modifying the
proof of the characterization of Hankel multipliers given by
the authors in Math. Ann. 342 (2008), 3168.

137148 
Random walks and the porous medium equation.
C. Cortázar, M. Elgueta, S. Martínez and J. D. Rossi
PDF
In this paper we consider a fixed initial condition
$u_0$ and we study the limit as $\varepsilon \rightarrow
0$ of $u_\varepsilon$, the solution to the rescaled problem
$$
u_t(x,y) = \frac{1}{\varepsilon^2}\left(\int_R
J\left(\frac{xy}{\varepsilon u(y,t)}\right)
\frac{dy}{\varepsilon}  u(x,t)\right)
\quad \text{in } R \times [0,\infty)
$$
with initial condition $u_\varepsilon(x, 0) = u_0(x)$.
Here $J$ is a smooth non negative even function supported in
the interval $[1, 1]$. Moreover it is assumed that $\int
J = 1$ and that $J$ is decreasing on $[0, 1]$.
We prove that, under adequate hypothesis on the initial
condition, the limit
$$
\lim_{\varepsilon\rightarrow 0} u_\varepsilon = u
$$
is the solution to the well known porous medium equation
$v_t = D(v^3)_{xx}$, with initial condition
$u_\varepsilon(x, 0) = u_0(x)$ for a suitable constant $D$.

149155 
Multilinear singular integral operators with variable
coefficients.
Rodolfo H. Torres
PDF
Some recent results for bilinear or multilinear singular integrals
operators are presented. The focus is on some of the results that can be viewed
as natural counterparts of classical theorems in CalderónZygmund theory,
adding to the already existing extensive literature in the subject. In particular,
two different classes of operators that can be seen as bilinear counterparts of
linear CalderónZygmund operators are considered. Some highlights of the
recent progress done for operators with variable coefficients are a modulation
invariant bilinear T1Theorem and some new weighted norm inequalities.

157174 
Schwartz functions on the Heisenberg group,
spectral multipliers and Gelfand pairs.
Fulvio Ricci
PDF
We review recent results proved jointly with B. Di Blasio and
F. Astengo. On the Heisenberg group $H_n$, consider the two
commuting selfadjoint operators $L$ and $i^{1}T$, where $L$
is the sublaplacian and $T$ is the central derivative. Their
joint $L^2$spectrum is the socalled Heisenberg fan, contained
in $\mathbb{R}^2$. To any bounded Borel function $m$ on the
fan, we associate the operator $m(L, i^{1}T)$. The main result
that we describe says that the convolution kernel of $m(L,
i^{1}T)$ is a Schwartz function if and only if $m$ is the
restriction of a Schwartz function on $\mathbb{R}^2$. We point
out that this result can be interpreted in terms of the
spherical transform for the convolution algebra of
$U(n)$invariant functions on $H_n$. We also describe
extensions to more general situations.

175186 
Hankel operators between HardyOrlicz spaces
and products of holomorphic functions.
Aline Bonami and Benoît Sehba
PDF
For $\mathbb{B}_n$ the unit ball of $\mathbb{C}^n$, we consider
HardyOrlicz spaces of holomorphic functions
$\mathcal{H}^\Phi$, which are preduals of spaces of BMOA
type with weight. We characterize the symbols of Hankel
operators that extend into bounded operators from the
HardyOrlicz $\mathcal{H}^{\Phi_1}$ into
$\mathcal{H}^{\Phi_2}$. We also consider the closely related
question of integrability properties of the product of two
functions, one in $\mathcal{H}^{\Phi_1}$ and the other one in
the dual of $\mathcal{H}^{\Phi_2}$.

187199 
Remarks on spectral multiplier theorems
on Hardy spaces associated with semigroups of operators.
Jacek Dziubański and Marcin Preisner
PDF
Let $L$ be a nonnegative, selfadjoint operator on
$L^2(\Omega)$, where $(\Omega, d, \mu)$ is a space of
homogeneous type. Assume that the semigroup $\{T_t\}_{t > 0}$
generated by $L$ satisfies Gaussian bounds, or more generally
DaviesGaffney estimates. We say that $f$ belongs to the Hardy
space $H^1_L$ if the square function
$$
S_h f(x) = \left( \iint_{\Gamma(x)}
t^2 L e^{t^2 L} f(y)^2
\frac{d\mu(y)}{\mu(B_d(x,t))}
\frac{dt}{t}
\right)^{1/2}
$$
belongs to $L^1(\Omega, d\mu)$, where $\Gamma(x) = \{(y, t) \in
\Omega \times (0, \infty) : d(x, y) < t\}$. We prove spectral
multiplier theorems for $L$ on $H^1_L$.

201215 
Optimal nonlinear models.
Akram Aldroubi, Carlos Cabrelli, and Ursula Molter
PDF
This paper is a survey about recent results on sparse
representations and optimal models in different settings.
Given a set of functions, we show that there exists an optimal
collection of subspaces minimizing the sum of the square of the
distances between each function and its closest subspace in the
collection. Further, this collection of subspaces gives the
best sparse representation for the given data, in a sense
defined later, and provides an optimal model for sampling in a
union of subspaces.

217225 
Nota sobre la vida y obra de L. A. Santaló.
A. M. Naveira y A. Reventós
PDF

227263 
