Current volume
Past 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

Volumen 52, número 1 (2011)
Eduardo H. Zarantonello (19182010).
J. Tirao
PDF

ivi 
De matemática y matemáticos.
Eduardo H. Zarantonello
PDF
Conferencia originalmente ofrecida en septiembre
de 1981 en Córdoba, Argentina, con motivo de la celebración del XXVº
aniversario de la creación del Instituto de Matemática, Astronomía y
Física de la Universidad Nacional de Córdoba.
Note: This text was not included in the print version of the Revista.

viixii 
Factor congruences in semilattices.
Pedro Sánchez Terraf
PDF
We characterize factor congruences in semilattices by using
generalized notions of order ideal and of direct sum of ideals. When the semilattice
has a minimum (maximum) element, these generalized ideals turn into
ordinary (dual) ideals.

110 
Properties of the bivariate confluent hypergeometric
function kind 1 distribution.
Daya K. Nagar and Fabio Humberto SepúlvedaMurillo
PDF
The bivariate confluent hypergeometric function
kind 1 distribution is defined by the probability density function
proportional to
x_{1}^{ν1 − 1} x_{2}^{ν2 − 1}_{1}F_{1}(α; β; −x_{1} − x_{2}).
In this article, we study several properties
of this distribution and derive density functions of X_{1}/X_{2},
X_{1}/(X_{1} + X_{2}),
X_{1} + X_{2} and 2 √(X_{1} X_{2}).
The density function of 2 √(X_{1} X_{2}) is represented in
terms of modified Bessel function of the second kind. We also show that for
ν_{1} − ν_{2} = 1/2, 2 √(X_{1} X_{2}) follows a
confluent hypergeometric function kind 1 distribution.

1121 
Ergodic properties of linear operators.
María Elena Becker
PDF
Let T be a bounded linear operator on a
Banach space X.
We prove some properties of X_{1} = { z ∈ X :
lim_{n} ∑_{k=1}^{n} (T^{k}z/k) exists}
and we construct an operator T such that
lim_{n} T^{n}/n = 0, but
(I − T)X is not included in X_{1}.

2325 
A new application of power increasing sequences.
Hüseyin Bor
PDF
In the present paper, we have proved a general summability factor
theorem by using a general summability method. This theorem also includes
several new results.

2732 
A note on integral Cparallel submanifolds
in S^{7}(c).
D. Fetcu and C. Oniciuc
PDF
We find the explicit parametric equations of the flat 3dimensional
integral Cparallel submanifolds in the sphere S^{7} endowed with the deformed
Sasakian structure defined by Tanno.

3345 
Weighted local BMO spaces and the local
HardyLittlewood maximal operator.
Aníbal Chicco Ruiz and Eleonor Harboure
PDF
We define a local type of a weighted BMO space on
R^{+}
and prove the boundedness of the local HardyLittlewood maximal function in
that space, provided that the weight belongs to the local class
A^{1}_{loc}.

4756 
Global L^{p} estimates
for degenerate OrnsteinUhlenbeck operators: a general approach.
Ermanno Lanconelli
PDF
We present a new approach to prove global
L^{p} estimates for degenerate OrnsteinUhlenbeck
operators in R^{N}.
We then show how to pave the way to extend such a technique to
classes of general Hörmander operators. Several historical notes
related to CalderónZygmund’s singular integrals theory in
Euclidean and in nonEuclidean settings are also provided.

5772 
Triality and the normal sections of Cartan’s
isoparametric hypersurfaces.
Cristián U. Sánchez
PDF
The present paper is devoted to study the algebraic sets of normal
sections of the so called Cartan’s isoparametric hypersurfaces
M_{R},
M_{C}, M_{H} and M_{O}
of complete flags in the projective planes RP^{2},
CP^{2}, HP^{2} and OP^{2}.
It presents a connection between “normed trialities” and the polynomial
defining the algebraic sets of normal sections of these hypersurfaces. It contains
also a geometric and topological description of these algebraic sets by means of the
isotropy actions of the isoparametric hypersurfaces.

7388 
Approximation and shape preserving properties of
the truncated Baskakov operator of maxproduct kind.
Barnabás Bede, Lucian Coroianu and Sorin G. Gal
PDF
Starting from the study of the Shepard nonlinear operator
of maxprod type in [2], [3], in the recent monograph [4], Open Problem 5.5.4, pp.
324326, the Baskakov maxprod type operator is introduced and the question
of the approximation order by this operator is raised. The aim of this note is
to obtain the order of uniform approximation Cω_{1}(f; 1/√n)
(with the explicit constant C = 24) of another operator called the
truncated maxprod Baskakov operator and to prove by a counterexample
that in some sense, for arbitrary
f this type of order of approximation with respect to
ω_{1}(f; √n) cannot be
improved. However, for some subclasses of functions including for example the
nondecreasing concave functions, the essentially better order of approximation
ω_{1}(f; 1/n) is obtained. Finally, some shape
preserving properties are proved.

89107 
Some Slater type inequalities for convex functions
of selfadjoint operators in Hilbert spaces.
S. S. Dragomir
PDF
Some inequalities of the Slater type for convex functions of selfadjoint
operators in Hilbert spaces $H$ under suitable assumptions for the involved
operators are given. Amongst others, it is shown that if $A$ is a positive
definite operator with $Sp(A) \subset [m,M]$ and $f$
is convex and has a continuous derivative on $[m,M]$, then for
any $x\in H$ with $\left\Vert x\right\Vert =1$ the following inequality
holds:
\begin{multline*}
0\leq f\left( \frac{\left\langle Af^{\prime }\left( A\right)
x,x\right\rangle }{\left\langle f^{\prime }\left( A\right) x,x\right\rangle }%
\right) \left\langle f\left( A\right) x,x\right\rangle \\
\leq \frac{1}{4}\cdot \sqrt{\frac{Mf^{\prime }\left( M\right) }{mf^{\prime
}\left( m\right) }}\left( Mm\right) \left( f^{\prime }\left( M\right)
f^{\prime }\left( m\right) \right).
\end{multline*}

109120 
Necessary and sufficient conditions for the Schur
harmonic convexity or concavity of the extended mean values.
WeiFeng Xia, YuMing Chu and GenDi Wang
PDF
In this paper, we prove that the extended values $E(r,s;x,y)$ are Schur
harmonic convex (or concave, respectively) with respect to
$(x,y)\in (0,\infty)\times(0,\infty)$ if and only if $(r,s)\in
\{(r,s):s\geq1, s\geq r,s+r+3\geq0\}\cup\{(r,s):r\geq1, r\geq
s,s+r+3\geq0\}$ (or $\{(r,s):s\leq1, r\leq1,s+r+3\leq0\},$
respectively).

121132 
Property (ω) and quasiclass (A, k)
operators.
M. H. M. Rashid
PDF
In this paper, we prove the following assertions:
(i) If T is of quasiclass (A, k), then T
is polaroid and reguloid;
(ii) If T or T^{*} is an algebraically
of quasiclass (A, k) operator, then Weyls theorem holds for
f(T) for every f ∈ Hol(σ(T));
(iii) If T^{*} is an algebraically of quasiclass
(A, k) operator, then aWeyls theorem holds for
f(T)
for every f ∈ Hol(σ(T));
(iv) If T^{*} is algebraically of quasiclass
(A, k) then property (ω) holds for T.

133142 
Solution of Troesch’s problem using
He’s polynomials.
Syed Tauseef MohyudDin
PDF
In this paper, we apply He’s polynomials
for finding the approximate solution of the Troesch’s problem
which arises in the confinement of a plasma column by radiation
pressure and applied physics. The proposed technique proved to be
very effective and is easier to implement as compare to decomposition method.

143148 
Julio Rey Pastor, su posición en la escuela
matemática argentina.
Eduardo L. Ortiz
PDF
This paper was read at the Tandil Meeting
of the UMA, in September 2010; in this presentation I keep to the
original format of a lecture.
I briefly consider three of the main attempts made in Argentina to establish
a mathematics school, between 1817 and 1940, paying more attention to the
third one, in which Julio Rey Pastor was the main character. Contrary to
the earlier ones, in this last period mathematics began to be established as
a distinct discipline, with its own problems and methods, while keeping close
ties with other disciplines. In this lecture I’ll also consider some matters that
emerged in parallel with these attempts, and make some remarks on the
different approaches used to tackle them. At the same time I’ll try to relate the
progress of mathematics in Argentina with the doctrines and ideas that, in
different periods of its history, dominated its cultural life.

149194 
Volumen 52, número 2 (2011)
This volume contains the contributed papers from the X^{th} Encuentro
Nacional de Analistas Alberto P. Calderón, which took place between
August 25th and 28th, 2010, in La Falda, Córdoba.
Preface.
Carlos Cabrelli and Eleonor Harboure
PDF

iiii 
Hardy spaces associated with semigroups of operators.
Jorge J. Betancor
PDF
This paper is a non exhaustive survey about Hardy
spaces defined by semigroups of operators.

122 
Sobolev spaces diversification.
Bruno Bongioanni
PDF
This work attempts to be an overview of a variety
of results concerning Sobolev spaces associated to some orthonormal systems,
particularly the Hermite and Laguerre operators settings.

2334 
Five basic lemmas for symmetric tensor products
of normed spaces.
Daniel Carando and Daniel Galicer
PDF
We give the symmetric version of five lemmas
which are essential for the theory of tensor products (and norms).
These are: the approximation, extension, embedding, density and local
technique lemma. Some applications of these tools to the metric theory
of symmetric tensor products and to the theory of polynomials ideals
are given.

3560 
Wiener’s lemma: pictures at an exhibition.
Ilya A. Krishtal
PDF
In this expository paper we present various general
extensions of the celebrated Wiener’s Tauberian Lemma, outline several
ingredients that are often used in proofs and discuss a few applications
to localization of frames.

6179 
Porosity, dimension, and local entropies: A survey.
Pablo Shmerkin
PDF
Porosity and dimension are two useful, but different,
concepts that quantify the size of fractal sets and measures. An active
area of research concerns understanding the relationship between these
two concepts. In this article we will survey the various notions of porosity
of sets and measures that have been proposed, and how they relate to
dimension. Along the way, we will introduce the idea of local entropy
averages, which arose in a different context, and was then applied to
obtain a bound for the dimension of mean porous measures.

81103 
Importance of Zak transforms for harmonic analysis.
Edward N. Wilson
PDF
In engineering and applied mathematics, Zak transforms have been
effectively used for over 50 years in various applied settings. As
Gelfand observed in a 1950 paper, the variable coefficient Fourier
series ideas articulated in Andre Weil’s famous book on integration
lead to an exceedingly elementary proof of the Plancherel Theorem for
LCA groups. The transform for functions on R appearing in Zak’s
seminal 1967 paper is actually a special case of the LCA group transforms
earlier introduced by Weil; Zak states this explicitly in his 1967
paper but the mathematical community nonetheless chose to name the
transform for him.
In brief, the properties of Zak transforms are simply reflections
of elementary Fourier series properties and the Plancherel Theorem
for noncompact LCA groups is an immediate consequence of the fact
that Fourier transforms are averages of Zak transforms. It is remarkable
that only a small handful of mathematicians know this proof and that
all textbooks continue to give much harder and less transparent proofs
for even the case of the group R. Generalized Zak transforms arise
naturally as intertwining operators for various representations of
Abelian groups and allow formulation of many appealing theorems.

105113 
