On the spectrum of isomorphisms defined on the space of smooth functions which are flat at 0

In this note we study the spectrum and the Waelbroeck spectrum of the derivative operator composed with isomorphic multiplication ope

The role of GPR techniques in determining ice cave properties: Peña Castil ice cave, Picos de Europa

Producción CientíficaThe structure and ice content of ice caves are poorly understood. Ground penetrating radar (GPR) can provide useful insights but has only rarely been applied to ice caves. This paper interprets GPR images (radargrams) in terms of internal structure, stratification, compaction, thickness and volume of the ice block in the Peña Castil ice cave (Central Massif of Picos de Europa, northern Spain), providing the endokarst geometry of the ice cave in GPR data reflections. Eight radargrams were obtained by applying a shielded ground‐coupled antenna with a nominal frequency of 400 MHz. Although the radargrams do not depict the ice–basal bedrock interface, they suggest that the ice block is at least 54 m deep and similarly thick. Some curved reflection signatures suggest a potential vertical displacement in the block of ice, and thus certain dynamics in the ice body. Other images show numerous interbedded clasts and thin sediment layers imaged as banded reflections. In this particular cave a direct visual inspection of the ice stratigraphy is a difficult task but GPR provides clear reflectivity patterns of some of its internal features, making GPR a suitable instrument for this and future studies to achieve a better and broader understanding of the internal behavior of ice caves.Ministerio de Economía, Industria y Competitividad (project CGL2015-68144-R)Ministerio de Agricultura y Pesca, Alimentación y Medio Ambiente (project OAPN-053/2010

Uniformly ergodic probability measures

Let $G$ be a locally compact group and $\mu$ be a probability measure on $G$. We consider the convolution operator $\lambda_1(\mu)\colon L_1(G)\to L_1(G)$ given by $\lambda_1(\mu)f=\mu \ast f$ and its restriction $\lambda_1^0(\mu)$ to the augmentation ideal $L_1^0(G)$. Say that $\mu$ is uniformly ergodic if the Ces\`aro means of the operator $\lambda_1^0(\mu)$ converge uniformly to 0, that is, if $\lambda_1^0(\mu)$ is a uniformly mean ergodic operator with limit 0 and that $\mu$ is uniformly completely mixing if the powers of the operator $\lambda_1^0(\mu)$ converge uniformly to 0. We completely characterize the uniform mean ergodicity of the operator $\lambda_1(\mu)$ and the uniform convergence of its powers and see that there is no difference between $\lambda_1(\mu)$ and $\lambda_1^0(\mu)$ in this regard. We prove in particular that $\mu$ is uniformly ergodic if and only if $G$ is compact, $\mu$ is adapted (its support is not contained in a proper closed subgroup of $G$) and 1 is an isolated point of the spectrum of $\mu$. The last of these three conditions is actually equivalent to $\mu$ being spread-out (some convolution power of $\mu$ is not singular). The measure $\mu$ is uniformly completely mixing if and only if $G$ is compact, $\mu$ is spread-out and the only unimodular value of the spectrum of $\mu$ is 1.Comment: Updated version. References to previous related results are improved. 21 page