Interpolation by Differences In H∞

We pose an interpolation problem for the space of bounded analytic functions in the disk. The interpolation is performed by a function and its di˛erence of values in points whose subscripts are related by an increasing application. We impose that the data values satisfy certain conditions related to the pseudohyperbolic distance, and characterize interpolating sequences in terms of uniformly separated subsequences.

Borel and Volume Classes for Dense Representations of Discrete Groups

We show that the bounded Borel class of any dense representation $\rho : G\to{\operatorname{PSL}}_n{\mathbb{C}}$ is non-zero in degree three bounded cohomology and has maximal semi-norm, for any discrete group $G$. When $n=2$, the Borel class is equal to the three-dimensional hyperbolic volume class. Using tools from the theory of Kleinian groups, we show that the volume class of a dense representation $\rho : G\to{\operatorname{PSL}}_2{\mathbb{C}}$ is uniformly separated in semi-norm from any other representation $\rho ^{\prime}: G\to{\operatorname{PSL}}_2 {\mathbb{C}}$ for which there is a subgroup $H\le G$ on which $\rho $ is still dense but $\rho ^{\prime}$ is discrete or indiscrete but stabilizes a point, line, or plane in ${\mathbb{H}}^3\cup \partial{\mathbb{H}}^3$. We exhibit a family of dense representations of a non-abelian free group on two letters and a family of discontinuous dense representations of ${\operatorname{PSL}}_2{\mathbb{R}}$, whose volume classes are linearly independent and satisfy some additional properties; the cardinality of these families is that of the continuum. We explain how the strategy employed may be used to produce non-trivial volume classes in higher dimensions, contingent on the existence of a family of hyperbolic manifolds with certain topological and geometric properties.

CARLESON INTERPOLATING SEQUENCES FOR BANACH SPACES OF ANALYTIC FUNCTIONS

This paper presents an approach, based on interpolation theory of operators, to the study of interpolating sequences for interpolation Banach spaces between Hardy spaces. It is shown that the famous Carleson result for H ∞ can be lifted to a large class of abstract Hardy spaces. A description is provided of the range of the Carleson operator defined on interpolation spaces between the classical Hardy spaces in terms of uniformly separated sequences. A key role in this description is played by some general interpolation results proved in the paper. As by-products, novel results are obtained which extend the Shapiro–Shields result on the characterisation of interpolation sequences for the classical Hardy spaces H p . Applications to Hardy–Lorentz, Hardy–Marcinkiewicz and Hardy–Orlicz spaces are presented.

Facile construction of an Ag0-doped Ag(I)-based coordination polymer via self-photoreduction strategy for enhanced visible light driven photocatalysis

Owing to the uniformly separated metal sites and regular structures, Ag(I)-based coordination polymers (CPs) have been considered as promising platforms for plasmonic photocatalysts. Herein, a novel Ag(I)-CP [Ag2(NO2-bdc)(4,4’-bpy)2]·2CH3CN·2.5H2O (JLNU-90, NO2-bdc...

A novel miniaturized log-periodic dipole array antenna using dynamic scaling factor for RFID application

A novel radio frequency identification antenna based on log-periodic dipole array (LPDA) antenna at 5.8 GHz is presented. The antenna design approach consists of two major steps. Firstly, the conventional primitive method is used to design a traditional LPDA antenna. The antenna structure is then miniaturized and its overall performance significantly improved. Dynamic scaling factor along with uniformly separated elements are introduced in this class of antenna, resulting in a 51.5% length reduction. To improve front-to-back (F/B) ratio a symmetrical folding technique is employed, leading to 21.5 dB F/B ratio for the fabricated prototype. An excellent level of input impedance matching (S11 = −28 dB) is achieved using a well-designed feeding system through a proximity coupling technique. The measured gain of the fabricated prototype is 6.2 dBi, and the overall dimension of the antenna substrate is only 30 × 45 mm2 (0.58λ0 × 0.87λ0).