Quasi-analyticity in Carleman ultraholomorphic classes

We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson's Lemma under an additional condition related to the growth index of the sequence.Comment: To appear in Ann. Inst. Fourier, Grenobl

Indices of O-regular variation for weight functions and weight sequences

A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure, obtained from a weight function or sequence subject to standard conditions entailing desirable properties (algebraic closure, stability under operators, interpolation, etc.) for the corresponding spaces. The aim of this paper is to stress or reveal the true nature of these diverse conditions imposed on weights, appearing in a scattered and disconnected way in the literature: they turn out to fall into the framework of O-regular variation, and many of them are equivalent formulations of one and the same feature. Moreover, we study several indices of regularity/growth for both functions and sequences, which allow for the rephrasing of qualitative properties in terms of quantitative statements.Comment: 37 page

A Phragm\'en-Lindel\"of theorem via proximate orders, and the propagation of asymptotics

We prove that, for asymptotically bounded holomorphic functions in a sector in $\mathbb{C}$, an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by A. Fruchard and C. Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragm\'en-Lindel\"of theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of E. Lindel\"of and G. Valiron.Comment: 20 page

The surjectivity of the Borel mapping in the mixed setting for ultradifferentiable ramification spaces

We consider r-ramification ultradifferentiable classes, introduced by J. Schmets and M. Valdivia in order to study the surjectivity of the Borel map, and later on also exploited by the authors in the ultraholomorphic context. We characterize quasianalyticity in such classes, extend the results of Schmets and Valdivia about the image of the Borel map in a mixed ultradifferentiable setting, and obtain a version of the Whitney extension theorem in this framework.Comment: 31 pages; this version has been accepted for publication in Monatsh. Mat

A theoretical insight into the catalytic effect of a mixed-metal oxide at the nanometer level: The case of the highly active metal/CeOx/TiO2(110) catalysts

The structural and electronic properties of CeOx species supported on the rutile TiO2 110 surface have been examined by means of periodic density-functional calculations that use a generalized gradient approximation functional including a Hubbard-like type correction. Deposition of Ce atoms leads in a first step to Ce3+ ions bound to the surface through bridge and in-plane oxygen atoms, the released electrons occupying the Ti 3d empty orbitals. Further addition of Ce and molecular oxygen gives place to Ce2O3 dimers diagonally arranged on the surface, in agreement with the spots observed in the scanning tunnel microscope images. The formation process of CeOx nanoparticles NPs on the TiO2 surface is highly exothermic and our calculations show that the redox properties of the Ce III-Ce IV couple are significantly altered when it is supported on TiO2. In particular the reactivity against CO/O2 indicates that on the surface the presence of Ce III is favored over Ce IV species. Our results also indicate that the CeOx /TiO2 interface should be seen like a real mixed-metal oxide rather than a supported NP of ceria. Finally, in the context of the high catalytic activity of the M /CeOx /TiO2 M =Au,Cu,Pt systems in the water-gas shift reaction, we have examined the dissociation of water on the CeOx /TiO2 surface and estimated a barrier as small as 0.04 eV, i.e. 8 times smaller than that computed for a TiO2 oxygen vacancy. This result agrees with the experimental superior catalytic activity of the M /CeOx /TiO2 systems over M /TiO2.Gobierno de España. Ministerio Ciencia e Innovación (MICINN) MAT2005-01872 y CSD2008-0023Junta de Andalucía FQM-132Departamento de Energía de EE. UU. División de Subvención de Ciencias Químicas DE-AC02-98CH1088