Search results for "esg"

Hilbert-Schmidt Hankel operators on the Segal-Bargmann space

2004

This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions onCn\mathbb {C}^nthat are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbolg∈L∞(Cn)g \in L^{\infty }(\mathbb {C}^n)the Hankel operatorHgH_gis of the Hilbert-Schmidt class if and only ifHg¯H_{\bar {g}}is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operatorsHgH_gandHg¯H_{\bar {g}}coincide. But, in general, if we deal with bounded symbols, only the inequality‖Hg‖HS≤2‖Hg¯‖HS\|H_g\|_{HS}\leq 2\|H_{\bar {g}}\|_{HS}can be proved. The resul…

Biweights on Partial *-Algebras

2000

This chapter is devoted to the systematic investigation of biweights on partial *-algebras. These are a generalization of invariant positive sesquilinear forms that still allows a Gel’fand—Naĭmark—Segal (GNS) construction of representations. In Section 9.1, we apply this GNS construction for biweights and we obtain *-representations and cyclic vector representations of partial *-algebras, and we give some examples of biweights. Section 9.2 is devoted to the investigation of the Radon—Nikodým theorem and the Lebesgue decomposition theorem for biweights on partial *-algebras. In Section 9.3, we define regular and singular biweights on partial *-algebras and we characterize them with help of t…

Dimension of self-affine sets for fixed translation vectors

2018

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

On the inverse absolute continuity of quasiconformal mappings on hypersurfaces

2018

We construct quasiconformal mappings $f\colon \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ for which there is a Borel set $E \subset \mathbb{R}^2 \times \{0\}$ of positive Lebesgue $2$-measure whose image $f(E)$ has Hausdorff $2$-measure zero. This gives a solution to the open problem of inverse absolute continuity of quasiconformal mappings on hypersurfaces, attributed to Gehring. By implication, our result also answers questions of V\"ais\"al\"a and Astala--Bonk--Heinonen.

Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

2015

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On density and π-weight of Lp(βN,R, μ)

2012

In Integration Theory, it is important to establish the separability or not of Lebesgue spaces of the type Lp, with 1 ≤ p < +∞. In general, the usual proof of this type of results for certain Lebesgue spaces, is conducted through methods of Real Analysis. In this work, we use some concepts and methods of pure General Topology in proving the non-separability of a particular Lebesgue space. Further, we provide some estimates for density and π-weight of such a space.

Assouad dimension, Nagata dimension, and uniformly close metric tangents

2013

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…

Gritos, y lamentos de las Almas del Purgatorio, que se cantan por la Ilustre Congregacion del Santísimo Christo del Buen-Acierto, en la Parroquial I…

1750

El full orlat Grav. xil. enmarcat de "El SS. Christo del Buen Acierto", flanquejat per altres grav. al·lusius al Purgatori El text del goig a tres col. separades per filets

Lamentos de las benditas Almas del Purgatorio, cuya Titular Patrona es la Serenísima Princesa del Sufragio, venerada en la Parroquial Iglesia de la …

1750

El full orlat Grav. xil. rectangular enmarcat de la Mare de Déu del Sufragi, flanquejat per grav. enmarcats més xicotets, també de forma rectangular, al·lusius al Purgatori Text del goig a tres col., separades per filets

Gritos, y lamentos de las Almas del Purgatorio, que se cantan por la Ilustre Congregacion del Santisimo Christo del Buen-Acierto, en la Parroquial Ig…

El full orlat Grav. xil. enmarcat de "El SS. Christo del Buen Acierto" , flanquejat per altres grav. al·lusius al Purgatori El text del goig a tres col. separades per filets