Local solvability
of elliptic equations of even order with Hölder coefficients.
María Amelia Muschietti and Federico Tournier
We consider elliptic equations of order $2m$ with Hölder coefficients. We
show local solvability of the Dirichlet problem with $m$ conditions on the
boundary of the upper half space. First we consider local solvability in free
space and then we treat the boundary case. Our method is based on applying the
operator to an approximate solution and iterating in the Hölder spaces. A
priori estimates for the approximate solution is the essential part of the
paper.

1–47 
On convergence
of subspaces generated by dilations of polynomials. An application to best
local approximation.
Fabián E. Levis and Claudia V. Ridolfi
We study the convergence of a net of subspaces generated by dilations of
polynomials in a finite dimensional subspace. As a consequence, we extend the
results given by Zó and Cuenya [Advanced Courses of Mathematical Analysis
II (Granada, 2004), 193–213, World Scientific, 2007] on a general
approach to the problems of best vectorvalued approximation on small regions
from a finite dimensional subspace of polynomials.

49–62 
Perturbation of Ruelle resonances and
Faure–Sjöstrand anisotropic space.
Yannick Guedes Bonthonneau
Given an Anosov vector field $X_0$, all sufficiently close vector fields are
also of Anosov type. In this note, we check that the anisotropic spaces
described by Faure and Sjöstrand and by Dyatlov and Zworski can be chosen
adapted to any smooth vector field sufficiently close to $X_0$ in $C^1$ norm.

63–72 
Generalized
metallic structures.
Adara M. Blaga and Antonella Nannicini
We study the properties of a generalized metallic, a generalized product and a
generalized complex structure induced on the generalized tangent bundle of a
smooth manifold $M$ by a metallic Riemannian structure $(J,g)$ on $M$,
providing conditions for their integrability with respect to a suitable
connection. Moreover, by using methods of generalized geometry, we lift $(J,g)$
to metallic Riemannian structures on the tangent and cotangent bundles of $M$,
underlying the relations between them.

73–86 
A heat conduction
problem with sources depending on the average of the heat flux on the
boundary.
Mahdi Boukrouche and Domingo A. Tarzia
Motivated by the modeling of temperature regulation in some mediums, we
consider the nonclassical heat conduction equation in the domain
$D=\mathbb{R}^{n1}\times\mathbb{R}^{+}$ for which the internal energy supply
depends on an average in the time variable of the heat flux $(y, s)\mapsto
V(y,s)= u_{x}(0, y, s)$ on the boundary $S=\partial D$. The solution to the
problem is found for an integral representation depending on the heat flux on
$S$ which is an additional unknown of the considered problem. We obtain that
the heat flux $V$ must satisfy a Volterra integral equation of the second kind
in the time variable $t$ with a parameter in $\mathbb{R}^{n1}$. Under some
conditions on data, we show that a unique local solution exists, which can be
extended globally in time. Finally in the onedimensional case, we obtain the
explicit solution by using the Laplace transform and the Adomian decomposition
method.

87–101 
On classes of finite rings.
Aleksandr Tsarev
A class of rings is a formation whenever it contains all homomorphic images of
its members and if it is subdirect product closed. In the present paper, it is
shown that the lattice of all formations of finite rings is algebraic and
modular. Let $R$ be a finite commutative ring with an identity element. It is
established that there is a onetoone correspondence between the set of all
invariant fuzzy prime ideals of $R$ and the set of all fuzzy prime ideals of
each ring of the formation generated by $R$.

103–111 
A canonical distribution on isoparametric submanifolds I.
Cristián U. Sánchez
We show that on every compact, connected homogeneous isoparametric
submanifold $M$ of codimension $h\geq 2$ in a Euclidean space, there
exists a canonical distribution which is bracket generating of step 2. An
interesting consequence of this fact is also indicated. In this first part
we consider only the case in which the system of restricted roots is
reduced, reserving for a second part the case of nonreduced restricted
roots.

113–130 
Second cohomology space
of $\mathfrak{sl}(2)$ acting on the space of bilinear bidifferential
operators.
Imed Basdouri, Sarra Hammami, and Olfa Messaoud
We consider the $\mathfrak{sl}(2)$module structure on the spaces
of bilinear bidifferential operators acting on the spaces of weighted
densities.
We compute the second cohomology group of the Lie algebra
$\mathfrak{sl}(2)$ with coefficients in the space of bilinear
bidifferential operators that act on tensor densities
$\mathcal{D}_{\lambda,\nu,\mu}$.

131–143 
Kreĭn space unitary dilations
of Hilbert space holomorphic semigroups.
Stefania A. M. Marcantognini
The infinitesimal generator $A$ of a strongly continuous semigroup on a Hilbert
space is assumed to satisfy that $B_\beta:=A\beta$ is a sectorial operator of
angle less than $\frac{\pi}{2}$ for some $\beta \geq 0$. If $B_\beta$ is
dissipative in some equivalent scalar product then the Naimark–Arocena
representation theorem is applied to obtain a Kreĭn space unitary dilation
of the semigroup.

145–160 
Lifting vector fields from manifolds
to $r$jet prolongation of the tangent bundle.
Jan Kurek and Włodzimierz M. Mikulski
If $m\geq 3$ and $r\geq 0$, we deduce that any natural linear operator lifting
vector fields from an $m$manifold $M$ to the $r$jet prolongation $J^{r}TM$ of the
tangent bundle $TM$ is the composition of the flow lifting $\mathcal{J}^r$
corresponding to the $r$jet prolongation functor $J^r$ with a natural linear
operator lifting vector fields from $M$ to $TM$. If $0\leq s\leq
r$ and $m\geq 3$, we find all natural linear operators transforming vector
fields on $M$ into basepreserving fibred maps $J^{r}TM\to J^{s}TM$.

161–168 
Localization operators and
scalogram associated with the generalized continuous wavelet transform on
$\mathbb{R}^d$ for the Heckman–Opdam theory.
Hatem Mejjaoli and Khalifa Trimèche
We consider the generalized wavelet transform $\Phi_{h}^{W}$ on $\mathbb{R}^{d}$ for
the Heckman–Opdam theory. We study the localization operators associated with
$\Phi_{h}^{W}$; in particular, we prove that they are in the Schatten–von
Neumann class. Next we introduce some results on the scalogram for this transform.

169–196 