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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 58, número 1 (2017)
June 2017
An interpolation theorem between CalderónHardy spaces.
Sheldy Ombrosi, Alejandra Perini, Ricardo Testoni
PDF
We obtain a complex interpolation theorem between weighted
CalderónHardy spaces for weights in a Sawyer class. The technique used is
based on the method obtained by J.O. Strömberg and A. Torchinsky; however, we
must overcome several technical difficulties associated with considering
onesided CalderónHardy spaces. Interpolation results of this type are
useful in the study of weighted weak type inequalities of strongly singular
integral operators.

119 
Quotient $p$Schatten metrics on spheres.
Esteban Andruchow, Andrea C. Antunez
PDF
Let $S(H)$ be the unit sphere of a Hilbert space $H$ and $U_p(H)$ the
group of unitary operators in $H$ such that $u1$ belongs to the
$p$Schatten ideal $B_p(H)$. This group acts smoothly and transitively
in $S(H)$ and endows it with a natural Finsler metric induced by the
$p$norm $\Vert z \Vert_p= \operatorname{tr}\left((z
z^*)^{p/2}\right)^{1/p}$.
This metric is given by \[ \Vert v \Vert_{x,p} = \min
\lbrace \Vert zy \Vert_p: y \in \mathfrak{g} _x \rbrace, \] where $z
\in \mathcal{B} _p(H)_ {ah}$ satisfies that $(d \pi_x)_1(z)=z \cdot x =
v$ and $ \mathfrak{g} _x$ denotes the Lie algebra of the subgroup of
unitaries which fix $x$. We call $z$ a lifting of $v$. A lifting $z_0$
is called a minimal lifting if additionally $ \Vert v \Vert_{x,p} =
\Vert z_0 \Vert_p$. In this paper we show properties of minimal
liftings and we treat the problem of finding short curves $ \alpha$
such that $ \alpha(0)=x $ and $ \dot{\alpha} (0)= v$ with $x \in S(H)$
and $v \in T_xS(H)$ given. Also we consider the problem of finding
short curves which join two given endpoints $x,y \in S(H)$.

2136 
Affine Szabó connections on smooth manifolds.
Abdoul Salam Diallo, Fortuné Massamba
PDF
We introduce a new structure, called affine Szabó connection. We prove
that, on $2$dimensional affine manifolds, the affine Szabó structure is
equivalent to one of the cyclic parallelisms of the Ricci tensor. A
characterization for locally homogeneous affine Szabó surfaces is obtained.
Examples of two and threedimensional affine Szabó manifolds are also given.

3752 
Connectedness of the algebraic set of vectors
generating planar normal sections of homogeneous isoparametric
hypersurfaces.
Cristián U. Sánchez
PDF
Let $M\subset \mathbb{S}^{n+1}\subset $ $\mathbb{R}^{n+2}$ be a homogeneous
isoparametric hypersurface and consider the algebraic set of unit tangent
vectors generating planar normal sections at a point $E\in M$ (denoted by
$\widehat{X}_{E}[M] \subset T_{E}(M)$). The present paper is devoted to prove
that $\widehat{X}_{E}[M]$ is connected by arcs. This in turn proves that
its projective image $X[M] \subset \mathbb{RP}(T_{E}(M))$ also has this
property.

5375 
Vanishing, Bass numbers, and cominimaxness of local
cohomology modules.
Jafar A'zami
PDF
Let $(R,m)$ be a commutative Noetherian regular local ring and $I$ be a proper
ideal of $R$. It is shown that $H^ {d1} _ \mathfrak{p} (R)=0$ for any
prime ideal $ \mathfrak{p} $ of $R$ with $ \dim(R/ \mathfrak{p})=2$,
whenever the set $ \{ n \in \mathbb{N} : R/ \mathfrak{p} ^ {(n)}$
is CohenMacaulay$\}$ is
infinite. Now, let $(R,m)$ be a commutative Noetherian unique factorization
local domain of dimension $d$, $I$ an ideal of $R$, and $M$ a finitely
generated $R$module. It is shown that the Bass numbers of the $R$module
$H^i_I(M)$ are finite, for all integers $i \geq 0$, whenever $
\operatorname{height} (I)=1$ or $d \leq 3$.

7783 
Soft ideals in ordered semigroups.
E. H. Hamouda
PDF
The notions of soft left and soft right ideals, soft quasiideal and soft
biideal in ordered semigroups are introduced. We show here that in ordered
groupoids the soft right and soft left ideals are soft quasiideals, and in
ordered semigroups the soft quasiideals are soft biideals. Moreover, we
prove that in regular ordered semigroups the soft quasiideals and the soft
biideals coincide. We finally show that in an ordered semigroup the soft
quasiideals are just intersections of soft right and soft left ideals.

8594 
On the Betti numbers of filiform Lie algebras over
fields of characteristic two.
Ioannis Tsartsaflis
PDF
An $n$dimensional Lie algebra $ \mathfrak{g} $ over a field $
\mathbb{F} $ of characteristic two is said to be of Vergne type
if there is a basis $e_1, \dots,e_n$ such that $ [e_1,e_i] =e_ {i+1} $
for all $2 \leq i \leq[e_i,e_j] n1$ and $ = c_ {i,j} e_ {i+j} $ for
some $c_ {i,j}
\in \mathbb{F} $ for all $i,j \ge 2$ with $i+j \le n$. We define the
algebra $ \mathfrak{m} _0$ by its nontrivial bracket relations: $
[e_1,e_i] =e_ {i+1} $, $2 \leq i \leq n1$, and the algebra $
\mathfrak{m} _2$: $ [e_1,e_i ] =e_ {i+1} $, $2 \le i \le[e_2, e_j ]
n1$, $ =e_ {j+2} $, $3 \le j \le n2$.
We show that, in contrast to
the corresponding real and complex cases, $ \mathfrak{m} _0(n)$ and $
\mathfrak{m} _2(n)$ have the same Betti numbers. We also prove that for
any Lie algebra of Vergne type of dimension at least $5$, there exists
a nonisomorphic algebra of Vergne type with the same Betti numbers.

95106 
Certain curves on some classes of threedimensional
almost contact metric manifolds.
Avijit Sarkar, Ashis Mondal
PDF
The object of the present paper is to characterize threedimensional
transSasakian generalized Sasakian space forms admitting biharmonic almost
contact curves with respect to generalized Tanaka Webster Okumura (gTWO)
connections and to give illustrative examples. The mean curvature vector of almost
contact curves has been analyzed on transSasakian manifolds with gTWO
connections. Some properties of slant curves on the same manifolds have been
established. Finally curvature and torsion, with respect to gTWO connections,
of Cparallel and Cproper slant curves in threedimensional almost contact
metric manifolds have been deduced.

107125 
Generalizations of Cline's formula for three generalized inverses.
Yong Jiang, Yongxian Wen, Qingping Zeng
PDF
It is shown that an element $a$ in a ring is Drazin invertible if and only if
so is $a^ {n} $; the Drazin inverse of $a$ is given by that of $a^ {n}
$, and vice versa. Using this result, we prove that, in the presence of
$aba=aca$, for any natural numbers $n$ and $m$, $(ac)^ {n} $ is Drazin
invertible in a ring if and only if so is $(ba)^ {m} $; the Drazin
inverse of $(ac)^ {n} $ is expressed by that of $(ba)^ {m} $, and vice
versa. Also, analogous results for the pseudo Drazin inverse and the
generalized Drazin inverse are established on Banach algebras.

127134 
Harmonic analysis associated with the modified
Cherednik type operator on the real line and PaleyWiener theorems
for its Hartley transform.
Hatem Mejjaoli
PDF
We consider a new differentialdifference operator $\Lambda$ on the
real line. We study the harmonic analysis associated with this
operator. Next, we establish the PaleyWiener theorems for its Hartley
transform on $\mathbb{R}$.

135162 
Elementary proof of the continuity of the topological
entropy at $\theta=\underline{1001}$ in the MilnorThurston
world.
Andrés Jablonski, Rafael Labarca
PDF
In 1965, Adler, Konheim and McAndrew introduced the topological entropy
of a given dynamical system, which consists of a real number that
explains part of the complexity of the dynamics of the system. In this
context, a good question could be if the topological entropy $H_{\mathrm{top}}
(f)$ changes continuously with $f$. For continuous maps this problem
was studied by Misisurewicz, Slenk and Urbański. Recently, and
related with the lexicographic and the MilnorThurston worlds, this
problem was studied by Labarca and others. In this paper we will
prove, by elementary methods, the continuity of the topological entropy
in a maximal periodic orbit ($ \theta= \underline{1001} $) in the
MilnorThurston world. Moreover, by using dynamical methods, we
obtain interesting relations and results concerning the largest
eigenvalue of a sequence of square matrices whose lengths grow up to
infinity.

163188 
Volumen 58, número 2 (2017)
December 2017
Geometric inequalities for Einstein totally real submanifolds in a complex space form.
Pan Zhang, Liang Zhang, Mukut Mani Tripathi
PDF
Two geometric inequalities are established for Einstein totally real
submanifolds in a complex space form. As immediate applications of
these inequalities, some nonexistence results are obtained.

189198 
Bézier variant of modified Srivastava–Gupta operators.
Trapti Neer, Nurhayat Ispir, Purshottam Narain Agrawal
PDF
Srivastava and Gupta proposed in 2003 a general family of linear positive
operators which include several well known operators as its special cases and
investigated the rate of convergence of these operators for functions of
bounded variation by using the decomposition techniques. Subsequently,
researchers proposed several modifications of these operators and studied their
various approximation properties. Yadav, in 2014, proposed a modification of
these operators and studied a Voronovskayatype approximation theorem and
statistical convergence. In this paper, we introduce the Bézier variant of the
operators defined by Yadav and give a direct approximation theorem by means of
the Ditzian–Totik modulus of smoothness and the rate of convergence for
absolutely continuous functions having a derivative equivalent to a function of
bounded variation. Furthermore, we show the comparisons of the rate of
convergence of the Srivastava–Gupta operators visàvis its Bézier
variant to a certain function by illustrative graphics using Maple algorithms.

199214 
Metallic shaped hypersurfaces in Lorentzian space forms.
Cihan Özgür, Nihal Yılmaz Özgür
PDF
We show that metallic shaped hypersurfaces in Lorentzian space forms are
isoparametric and obtain their full classification.

215226 
Friezes of type $\mathbb{D}$.
Kodjo Essonana Magnani
PDF
We establish a link between the values of a frieze of type
$\mathbb{D}_{n}$ and some values of a particular frieze of type
$\mathbb{A}_{2n1}$. This link allows us to compute, independently of each
other, all the cluster variables in the cluster algebra associated with a
quiver $Q$ of type $\mathbb{D}_{n}$.

227243 
Large images of reducible Galois representations.
Aftab Pande
PDF
Given a reducible Galois representation $\overline{\rho}: G_{\mathbb{Q}}
\rightarrow GL_2( \mathbb{F}_q)$ we show that there exists an irreducible
deformation $\rho : G_{\mathbb{Q}} \rightarrow GL_2 (\mathbb{W} [[T_1, T_2,\dots,
T_r,\dots]])$ of $\overline{\rho}$ ramified at infinitely many primes, where
$\mathbb{W}$ denotes the ring of Witt vectors of $\mathbb{F}_q$. This is a
modification of Ramakrishna's result for the irreducible case.

245251 
A note on weighted inequalities for a onesided maximal
operator in $\mathbb{R}^n$.
María Lorente, Francisco J. MartínReyes
PDF
We introduce a new dyadic onesided maximal operator $M_d^ {+\dots +} $ in $
\mathbb{R} ^n$ that allows us to obtain good weights for the $L^p$boundedness
of a onesided maximal operator $N^ {+\dots +} $ in $ \mathbb{R} ^n$, which is
equivalent to the classical onesided Hardy–Littlewood maximal operator in the
case $n=1$, but not in the case $n > 1$. In order to do this, we characterize the
good pairs of weights for the weak and strong type inequalities for $M_d^
{+\dots +} $ and we use a Fefferman–Stein type inequality which gives that, in
a certain sense, $M_d^ {+\dots +} $ controls $N^ {+\dots +} $.

253258 
Higher order elliptic equations in half space.
María Amelia Muschietti, Federico Tournier
PDF
We consider $2m^ \text{th} $ order elliptic equations with Hölder coefficients
in half space. We solve the Dirichlet problem with $m$ conditions on the
boundary of the upper half space. We first analyze the constant coefficient
case, finding the Green function and a representation formula, and then prove
Schauder estimates.

259280 
Fractional type integral operators of variable order.
Pablo Rocha, Marta Urciuolo
PDF
We study the boundedness on the variable Lebesgue spaces of the operators of
variable order \[ T_ {\Omega} f(x) = \int_{\Omega} yA_ {1} x^ {\alpha_{1}
(y)} \dots{m} yA_ x^ {\alpha_{m} (y)} f(y) \, dy \] and \[ U_ {\Omega} f(x)
= \int_{\Omega} yA_ {1} x^ {\alpha_{1} (x)} \dots{m} yA_ x^ {\alpha_{m}
(x)} f(y) \, dy, \] where $ \alpha_{i} : \Omega \subset \mathbb{R} ^ {n}
\rightarrow(0,n)$ are positive measurable functions, for $i=1, \dots, m$ $(m
\geq2)$, such that $ \alpha_{1} (x) + \dots + \alpha_{m} (x) = n  \alpha(x)$
with $0 \leq \alpha(x) < n$ for all $x \in \Omega$, and the $A_{i}$’s
are $n \times n$ invertible real matrices such that $A_ {i}  A_ {j} $ is
invertible if $i \neq j$.

281296 
The initial value problem for the Schrödinger equation
involving the Henstock–Kurzweil integral.
Salvador SánchezPerales
PDF
Let $L$ be the onedimensional Schrödinger operator defined by $Ly=y''+qy$.
We investigate the existence of a solution to the initial value problem for the
differential equation $(L \lambda)y=g$, when $q$ and $g$ are
Henstock–Kurzweil integrable functions on $ [a,b] $. Results presented in this
article are generalizations of classical results for the Lebesgue integral.

297306 
Threedimensional almost coKähler manifolds with
harmonic Reeb vector fields.
Wenjie Wang, Ximin Liu
PDF
Let $M^3$ be a threedimensional almost coKähler manifold whose Reeb vector
field is harmonic. We obtain some local classification results
of $M^3$ under some additional conditions related to the Ricci tensor.

307317 
Geometry of the projective unitary group of a $C^*$algebra.
Esteban Andruchow
PDF
Let $ \mathcal{A} $ be a $C^*$algebra with a faithful state $ \varphi$. It is
proved that the projective unitary group $ \mathbb{P} \, \mathcal{U} _
\mathcal{A} $ of $ \mathcal{A} $, \[ \mathbb{P} \, \mathcal{U} _ \mathcal{A} =
\mathcal{U} _ \mathcal{A} / \mathbb{T} .1, \] ($ \mathcal{U} _ \mathcal{A} $
denotes the unitary group of $ \mathcal{A} $) is a $C^ \infty$submanifold of
the Banach space $ \mathcal{B} _s( \mathcal{A})$ of bounded operators acting in
$ \mathcal{A} $, which are symmetric for the $ \varphi$inner product, and are
usually called symmetrizable linear operators in $ \mathcal{A} $.
A quotient
Finsler metric is introduced in $ \mathbb{P} \, \mathcal{U} _ \mathcal{A} $,
following the theory of homogeneous spaces of the unitary group of a
$C^*$algebra. Curves of minimal length with any given initial conditions are
exhibited. Also it is proved that if $ \mathcal{A} $ is a von Neumann algebra
(or more generally, an algebra where the unitary group is exponential) two
elements in $ \mathbb{P} \, \mathcal{U} _ \mathcal{A} $ can be joined by a
minimal curve.
In the case when $ \mathcal{A} $ is a von Neumann algebra with
a finite trace, these minimality results hold for the quotient of the metric
induced by the $p$norm of the trace ($p \ge 2$), which metrizes the strong
operator topology of $ \mathbb{P} \, \mathcal{U} _ \mathcal{A} $.

319329 
An extension of best $L^2$ local approximation.
Héctor H. Cuenya, David E. Ferreyra, Claudia V. Ridolfi
PDF
We introduce two classes of functions, one containing the class
of $L^2$ differentiable functions, and another containing the class of $L^2$
lateral differentiable functions. For functions in these new classes we prove
existence of best local approximation at several points. Moreover, we get
results about the asymptotic behavior of the derivatives of the net of best
approximations, which are unknown even for $L^2$ differentiable functions.

331342 
