Convolutions, multipliers and maximal regularity on vector-valued Hardy spaces

We extend the recently developed L^p-theory for the maximal regularity of the abstract Cauchy problem and the related Fourier multiplier techniques to the real-variable Hardy space H¹. Some results for H^p, 0 < p < 1, are also proved.     

A Library of Late Transition Metal Alloy Dielectric Functions for Nanophotonic Applications

Accurate complex dielectric functions are critical to accelerate the development of rationally designed metal alloy systems for nanophotonic applications, and to thereby unlock the potential of alloying for tailoring nanostructure optical properties. To date, however, accurate alloy dielectric functions are widely lacking. Here, a time‐dependent density‐functional theory computational framework is employed to compute a comprehensive binary alloy dielectric function library for the late transition metals most commonly employed in plasmonics (Ag, Au, Cu, Pd, Pt). Excellent agreement is found between electrodynamic simulations based on these dielectric functions and selected alloy systems experimentally scrutinized in 10 at% composition intervals. Furthermore, it is demonstrated that the dielectric functions can vary in very non‐linear fashion with composition, which paves the way for non‐trivial optical response optimization by tailoring material composition. The presented dielectric function library is thus a key resource for the development of alloy nanomaterials for applications in nanophotonics, optical sensors, and photocatalysis.     

Vector-valued multiparameter singular integrals and pseudodifferential operators

We consider multiparameter singular integrals and pseudodifferential operators acting on mixed-norm Bochner spaces Lp₁,…,pN(Rn₁×?×RnN;X) where X is a UMD Banach space satisfying Pisier's property (α). These geometric conditions are shown to be necessary. We obtain a vector-valued version of a result by R. Fefferman and Stein, also providing a new, inductive proof of the original scalar-valued theorem. Then we extend a result of Bourgain on singular integrals in UMD spaces with an unconditional basis to a multiparameter situation. Finally we carry over a result of Yamazaki on pseudodifferential operators to the Bochner space setting, improving the known vector-valued results even in the one-parameter case.     

On the necessity of property (α) for some vector-valued multiplier theorems

The notion of R-bounded operator families has proven to be crucial to several aspects of vector-valued Harmonic Analysis and its applications to PDEs. Concrete and important R-bounded sets have been identified among operators acting on UMD Banach spaces, which in addition enjoy G. Pisier’s property (α). We prove the necessity of (α) for a number of conclusions of this kind, complementing analogous results of G. Lancien in the product-space theory of Fourier multipliers and H ^∞-calculus. Received: 24 January 2007 Revised: 1 June 2007     

Spatial persistence of angular correlations in amyloid fibrils

Using atomic force microscopy height maps, we resolve and quantify torsional fluctuations in one-dimensional amyloid fibril aggregates self-assembled from three different representative polypeptide systems. Furthermore, we show that angular correlation in these nanoscale structures is maintained over several microns, corresponding to many thousands of molecules along the fibril axis. We model disorder in the fibril in respect of both thermal fluctuations and structural defects, and determine quantitative values for the defect density, as well as the energy scales involved in the fundamental interactions stabilizing these generic structures.     

Solid-phase synthesis of 7-substituted 3H-imidazo[2,1-i]purines

A method for solid-supported synthesis of N,N-disubstituted (3H-imidazo[2,1-i]purin-7-yl)methyl amines has been developed. The key features of this library synthesis are: (i) immobilization of commercially available N6-benzoyl-5'-O-(4,4'-dimethoxytrityl)-2'-deoxyadenosine 3'-(2-cyanoethyl N,N-diisopropylphosphoramidite) by phosphitylation to a hydroxyl-functionalized support, (ii) quantitative conversion of the deprotected adenine base to 3H-imidazo[2,1-i]purine-7-carbaldehyde with bromomalonaldehyde in DMF in the presence of formic acid and 2,6-lutidine, (iii) reductive amination of the formyl group followed by N-alkylation or N-acylation, and (iv) release from the support by acidolytic cleavage of the N-glycosidic bond. Steps (ii) and (iii) have been optimized in some detail by using (adenin-9-yl)acetic acid anchored to a Phe-Wang resin as a model compound.