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Claudio Mele

Publications and source records attributed to Claudio Mele.

10 recordsLinked to original sources
arXiv2025

Spectral and ergodic properties of the operator $B(r,s)$ over power series spaces $\Lambda_\infty(\alpha)$ of infinite type and their duals

In this paper, we investigate the spectral and ergodic properties of the linear operator $B(r,s)$ acting on power series spaces $\Lambda_\infty(\alpha)$ of infinite type and on their strong duals. Precisely, we provide a complete characterization of its fine spectrum and establish necessary and sufficient conditions for the operator to be power bounded and (uniformly) mean ergodic.

math.FA↗
arXiv2024

Mutual estimates of time-frequency representations and uncertainty principles

In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical $L^p$ spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations.

math.FA↗
arXiv2021

Spectra and ergodic properties of multiplication and convolution operators on the space $\mathcal{S}(\mathbb{R})$

In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions, i.e., operators of the form $M_h: \mathcal{S}(\mathbb{R})\to\mathcal{S}(\mathbb{R})$, $f \mapsto h f $, and $C_T\colon \mathcal{S}(\mathbb{R})\to\mathcal{S}(\mathbb{R})$, $f\mapsto T\star f$. Precisely, we determine their spectra and characterize when those operators are power bounded and mean ergodic.

math.FA↗
arXiv2021

Convolutors on $\mathcal{S}_ω(\mathbb{R}^N)$

In this paper we continue the study of the spaces $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ and $\mathcal{O}_{C,ω}(\mathbb{R}^N)$ undertaken in [1]. We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ is the space of convolutors of the space $\mathcal{S}_ω(\mathbb{R}^N)$ of the $ω$-ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $\mathcal{S}'_ω(\mathbb{R}^N)$. We also establish that the Fourier transform is an isomorphism from $\mathcal{O}'_{C,ω}(\mathbb{R}^N)$ onto $\mathcal{O}_{M,ω}(\mathbb{R}^N)$. In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $\mathcal{L}_b(\mathcal{S}_ω(\mathbb{R}^N))$ and the last space is endowed with its natural lc-topology.

math.FA↗
arXiv2020

Regularity of global solutions of partial differential equations in non isotropic ultradifferentiable spaces via time-frequency methods

In this paper we study regularity of partial differential equations with polynomial coefficients in non isotropic Beurling spaces of ultradifferentiable functions of global type. We study the action of transformations of Gabor and Wigner type in such spaces and we prove that a suitable representation of Wigner type allows to prove regularity for classes of operators that do not have classical hypoellipticity properties.

math.AP↗
arXiv2020

Multipliers on $\mathcal{S}_ω(\mathbb{R}^N)$

The aim of this paper is to introduce and to study the space $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ of the multipliers of the space $\mathcal{S}_ω(\mathbb{R}^N)$ of the $ω$-ultradifferentiable rapidly decreasing functions of Beurling type. We determine various properties of the space $\mathcal{O}_{M,ω}(\mathbb{R}^N)$. Moreover, we define and compare some lc-topologies of which $\mathcal{O}_{M,ω}(\mathbb{R}^N)$ can be naturally endowed.

math.FA↗
arXiv2019

In Situ Electrochemical SFG/DFG Study of CN-- and Nitrile Adsorption at Au from 1-Butyl-1-methyl-pyrrolidinium Bis(trifluoromethylsulfonyl) Amide Ionic Liquid ([BMP][TFSA]) Containing 4-{2-[1-(2-Cyanoethyl)-1,2,3,4-tetrahydroquinolin-6-yl]diazenyl} Benzonitrile (CTDB) and K[Au(CN)$_2$]

In this paper we report an in situ electrochemical Sum-/Difference Frequency Generation (SFG/DFG) spectroscopy investigation of the adsorption of nitrile and CN -- from the ionic liquid 1-butyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl) amide ([BMP][TFSA]) containing 4-{2-[1-(2-cyanoethyl)-1,2,3,4-tetrahydroquinolin-6-yl]-diazenyl}benzonitrile (CTDB) at Au electrodes in the absence and in the presence of the Au-electrodeposition process from K[Au(CN)$_2$ ]. The adsorption of nitrile and its coadsorption with CN -- resulting either from the cathodic decomposition of the dye or from ligand release from the Au(I) cyanocomplex yield potential-dependent single or double SFG bands in the range 2,125-2,140 cm$^{-1}$, exhibiting Stark tuning values of ca. 3 and 1 cm$^{-1}$ V$^{-1}$ in the absence and presence of electrodeposition, respectively. The low Stark tuning found during electrodeposition correlates with the cathodic inhibiting effect of CTDB, giving rise to its levelling properties. The essential insensitivity of the other DFG parameters to the electrodeposition process is due to the growth of smooth Au.

physics.chem-ph↗
arXiv2007

A SERS Investigation of Cyanide Adsorption and Reactivity during the Electrodeposition of Gold, Silver and Copper from Aqueous Cyanocomplexes Solutions

In this paper we report on the reactivity of adsorbed cyanide deriving from ligand release during metal electrodeposition from cyanocomplex solutions of Au(I), Au(III), Ag(I) and Cu(I) in H2O and D2O. When CN is adsorbed at cathodic potentials in excess of the HER threshold, metal-dependent reactivity can be detected by SERS. Finite surface coverages with adsorbed CN at such cathodic potentials can be obtained only if CN is delivered directly to the cathode surface as by decomplexing of the cyanocomplexes of the metals undergoing cathodic reduction. In Au(I) and Au(III) baths, Au-CN reacts with Au-H and is hydrogenated to adsorbed CH2=NH and CH3-NH2. In Ag(I) baths, Ag-CN reacts with Ag-H giving rise to polycyanogens. No reactivity of Cu-CN was found, under otherwise identical conditions. Our conclusions are supported also by dedicated DFT molecular computations.

cond-mat.mtrl-sci↗