The Essential Norm of Operators on Aαp(Bn)A^p_\alpha(\mathbb{B}_n)

In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1-1$. The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.Comment: v1: 32 pages; v2: 32 pages, typos corrected; v3: 32 pages, typos corrected, presentation improved based on referee comment

Power spectra of velocities and magnetic fields on the solar surface and their dependence on the unsigned magnetic flux density

We have performed power spectral analysis of surface temperatures, velocities, and magnetic fields, using spectro-polarimetric data taken with the Hinode Solar Optical Telescope. When we make power spectra in a field-of-view covering the super-granular scale, kinetic and thermal power spectra have a prominent peak at the granular scale while the magnetic power spectra have a broadly distributed power over various spatial scales with weak peaks at both the granular and supergranular scales. To study the power spectra separately in internetwork and network regions, power spectra are derived in small sub-regions extracted from the field-of-view. We examine slopes of the power spectra using power-law indices, and compare them with the unsigned magnetic flux density averaged in the sub-regions. The thermal and kinetic spectra are steeper than the magnetic ones at the sub-granular scale in the internetwork regions, and the power-law indices differ by about 2. The power-law indices of the magnetic power spectra are close to or smaller than -1 at that scale, which suggests the total magnetic energy mainly comes from either the granular scale magnetic structures or both the granular scale and smaller ones contributing evenly. The slopes of the thermal and kinetic power spectra become less steep with increasing unsigned flux density in the network regions. The power-law indices of all the thermal, kinetic, and magnetic power spectra become similar when the unsigned flux density is larger than 200 Mx cm^-2.Comment: 9 pages, 6 figures, accepted for publication in Ap

Symmetry-induced interference effects in metalloporphyrin wires

Organo-metallic molecular structures where a single metallic atom is embedded in the organic backbone are ideal systems to study the effect of strong correlations on their electronic structure. In this work we calculate the electronic and transport properties of a series of metalloporphyrin molecules sandwiched by gold electrodes using a combination of density functional theory and scattering theory. The impact of strong correlations at the central metallic atom is gauged by comparing our results obtained using conventional DFT and DFT+U approaches. The zero bias transport properties may or may not show spin-filtering behavior, depending on the nature of the d state closest to the Fermi energy. The type of d state depends on the metallic atom and gives rise to interference effects that produce different Fano features. The inclusion of the U term opens a gap between the d states and changes qualitatively the conductance and spin-filtering behavior in some of the molecules. We explain the origin of the quantum interference effects found as due to the symmetry-dependent coupling between the d states and other molecular orbitals and propose the use of these systems as nanoscale chemical sensors. We also demonstrate that an adequate treatment of strong correlations is really necessary to correctly describe the transport properties of metalloporphyrins and similar molecular magnets