1,603 research outputs found
Fourier multipliers in Hilbert spaces
This is a survey on a notion of invariant operators, or Fourier multipliers
on Hilbert spaces. This concept is defined with respect to a fixed partition of
the space into a direct sum of finite dimensional subspaces. In particular this
notion can be applied to the important case of where is a compact
manifold endowed with a positive measure. The partition in this case comes
from the spectral properties of a a fixed elliptic operator .Comment: These notes are based on our paper arXiv:1404.6479 (to appear in J.
Anal. Math.) and have been prepared for the instructional volume associated
to the Summer School on Fourier Integral Operators held in Ouagadougou,
Burkina Faso, where the authors took part during 14-26 September 201
Kernel and symbol criteria for Schatten classes and -nuclearity on compact manifolds
In this note we present criteria on both symbols and integral kernels
ensuring that the corresponding operators on compact manifolds belong to
Schatten classes. A specific test for nuclearity is established as well as the
corresponding trace formulae. In the special case of compact Lie groups, kernel
criteria in terms of (locally and globally) hypoelliptic operators are also
given. A notion of an invariant operator and its full symbol associated to an
elliptic operator are introduced. Some applications to the study of
-nuclearity on spaces are also obtained.Comment: 8 pages. arXiv admin note: substantial text overlap with
arXiv:1404.647
Lp-Nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups
Given a compact Lie group , in this paper we give symbolic criteria for
operators to be nuclear and r-nuclear on Lp-spaces, with applications to
distribution of eigenvalues and trace formulae. Since criteria in terms of
kernels are often not effective in view of Carleman's example, in this paper we
adopt the symbolic point of view. The criteria here are given in terms of the
concept of matrix symbols defined on the non-commutative analogue of the phase
space , where is the unitary dual of .Comment: This is the second half of our paper arXiv:1303.3914 so there is
overlap in the preliminaries sectio
Schatten classes on compact manifolds: Kernel conditions
In this paper we give criteria on integral kernels ensuring that integral
operators on compact manifolds belong to Schatten classes. A specific test for
nuclearity is established as well as the corresponding trace formulae. In the
special case of compact Lie groups, kernel criteria in terms of (locally and
globally) hypoelliptic operators are also given.Comment: 22 page
The bounded approximation property of variable Lebesgue spaces and nuclearity
In this paper we prove the bounded approximation property for variable
exponent Lebesgue spaces, study the concept of nuclearity on such spaces and
apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply
the obtained results to derive criteria for nuclearity and trace formulae for
periodic operators on in terms of global symbols.Comment: 18 pages. The paper has been updated by adding a remark (on page 6)
on a link between bounded and metric approximation properties. This should be
the final version to appear in Math Scan
Introducción a la responsabilidad de los profesionales de Enfermería: Revisión y análisis de sentencias sobre responsabilidad profesional sanitaria
En los últimos años el número de demandas contra el personal de enfermería ha experimentado un importante aumento debido en gran parte a la adquisición de nuevas competencias que ha experimentado la profesión, así como a la disminución del temor que en otras épocas han podido tener determinadas profesiones relacionadas con el ámbito de la salud y a un aumento de las exigencias sociales, que han hecho que las profesiones del ámbito de la sanidad estén, en muchos casos, en el punto de mira de la sociedad.
El punto de partida de este trabajo es el reconocimiento de que la enfermería es hoy en día una profesión con características propias y con todas las responsabilidades que ello supone y pretende hacer conscientes a estos profesiones de las consecuencias que puede tener el desarrollo de una mala praxis para evitar conductas que puedan desencadenar circunstancias condenables y situaciones difíciles desde el punto de vista profesional.
A lo largo de este trabajo, pretendo hacer una introducción sobre de los diferentes tipos de responsabilidad profesional que existen y que pueden afectar a los expertos de la enfermería y analizaré dos sentencias judiciales que enjuician algunas actuaciones de estos profesionales.Departamento de EnfermeríaGrado en Enfermerí
Practical Aspects of Allogeneic Hematopoietic Cell Transplantation for Patients with Poor-risk Chronic Lymphocytic Leukemia
Allogeneic hematopoietic cell transplantation has become a viable option for younger patients with poor-risk chronic lymphocytic leukemia. The results obtained with either conventional or reduced-intensity conditioning regimens have been recently evaluated and compared with alternative nontransplant strategies. This manuscript deals with practical aspects of the procedure, including patient and donor selection, conditioning regimen, GVHD prophylaxis, disease monitoring, infectious and noninfectious complications, and timing of the procedure. Finally, we speculate on how we could improve the results obtained with the procedure and new advances currently in clinical trials
Schatten classes and traces on compact groups
In this paper we present symbolic criteria for invariant operators on compact
topological groups characterising the Schatten-von Neumann classes
for all . Since it is known that for
pseudo-differential operators criteria in terms of kernels may be less
effective (Carleman's example), our criteria are given in terms of the
operators' symbols defined on the noncommutative analogue of the phase space
, where is a compact topological (or Lie) group and
is its unitary dual. We also show results concerning general
non-invariant operators as well as Schatten properties on Sobolev spaces. A
trace formula is derived for operators in the Schatten class .
Examples are given for Bessel potentials associated to sub-Laplacians (sums of
squares) on compact Lie groups, as well as for powers of the sub-Laplacian and
for other non-elliptic operators on SU(2) and on SO(3).Comment: 18 pages, updated final version, to appear in Math. Res. Letter
Boundedness of the dyadic maximal function on graded Lie groups
Let and let It was proved independently by C.
Calder\'on, R. Coifman and G. Weiss that the dyadic maximal function
\begin{equation*}
\mathcal{M}^{d\sigma}_Df(x)=\sup_{j\in\mathbb{Z}}\left|\smallint\limits_{\mathbb{S}^{n-1}}f(x-2^jy)d\sigma(y)\right|
\end{equation*} is a bounded operator on where
is the surface measure on In this paper we prove an
analogue of this result on arbitrary graded Lie groups. More precisely, to any
finite Borel measure with compact support on a graded Lie group
we associate the corresponding dyadic maximal function
using the homogeneous structure of the group. Then,
we prove a criterion in terms of the order (at zero and at infinity) of the
group Fourier transform of with respect to a
fixed Rockland operator on that assures the boundedness of
on for all Comment: 26 Page
- …