arXiv subjects
Publications and source records attributed to Jaime San Martín.
For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in Böchner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\in(1,\infty)$ and even approximatively norm-compact under stronger hypothesis.
For any $p\in[1,\infty]$, we prove that the set of simple functions taking at most $k$ different values is proximinal in $L^p$ for all $k\geq 1$. We introduce the class of uniformly approximable subsets of $L^p$, which is larger than the class of uniformly integrable sets. This new class is characterized in terms of the $p$-variation if $p\in[1,\infty)$ and in terms of covering numbers if $p=\infty$. We study properties of uniformly approximable sets. In particular, we prove that the convex hull of a uniformly approximable bounded set is also uniformly approximable and that this class is stable under Hölder transformations. We also prove that, for $p\in [1,\infty)$, the unit ball of $L^p$ is uniformly approximable if and only if $L^p$ is finite-dimensional, while for $p=\infty$ the unit ball is always uniformly approximable.
In this article we study stability properties of $g_O$, the standard Green kernel for $O$ an open regular set in $R^d$. In $d\ge 3$ we show that $g_O^β$ is again a Green kernel of a Markov Feller process, for any power $β\in [1,d/(d-2))$. In dimension $d=2$, if $O$ is an open Greenian regular set, we show the same result for $g_O^β$, for any $β\ge 1$ and for the kernel $\exp(αg_O)$, when $α\in (0,2π)$.
The High Cadence Transient Survey (HiTS) aims to discover and study transient objects with characteristic timescales between hours and days, such as pulsating, eclipsing and exploding stars. This survey represents a unique laboratory to explore large etendue observations from cadences of about 0.1 days and to test new computational tools for the analysis of large data. This work follows a fully \textit{Data Science} approach: from the raw data to the analysis and classification of variable sources. We compile a catalog of ${\sim}15$ million object detections and a catalog of ${\sim}2.5$ million light-curves classified by variability. The typical depth of the survey is $24.2$, $24.3$, $24.1$ and $23.8$ in $u$, $g$, $r$ and $i$ bands, respectively. We classified all point-like non-moving sources by first extracting features from their light-curves and then applying a Random Forest classifier. For the classification, we used a training set constructed using a combination of cross-matched catalogs, visual inspection, transfer/active learning and data augmentation. The classification model consists of several Random Forest classifiers organized in a hierarchical scheme. The classifier accuracy estimated on a test set is approximately $97\%$. In the unlabeled data, $3\,485$ sources were classified as variables, of which $1\,321$ were classified as periodic. Among the periodic classes we discovered with high confidence, 1 $δ$-scutti, 39 eclipsing binaries, 48 rotational variables and 90 RR-Lyrae and for the non-periodic classes we discovered 1 cataclysmic variables, 630 QSO, and 1 supernova candidates. The first data release can be accessed in the project archive of HiTS.
We report the discovery of distant RR Lyrae stars, including the most distant known in the Milky Way, using data taken in the $g-$band with the Dark Energy Camera as part of the High cadence Transient Survey (HiTS; 2014 campaign). We detect a total of 173 RR Lyrae stars over a ~120 deg^2 area, including both known RR Lyrae and new detections. The heliocentric distances d_H of the full sample range from 9 to >200 kpc, with 18 of them beyond 90 kpc. We identify three sub-groups of RR Lyrae as members of known systems: the Sextans dwarf spheroidal galaxy, for which we report 46 new discoveries, and the ultra-faint dwarf galaxies Leo IV and Leo V. Following an MCMC methodology, we fit spherical and ellipsoidal profiles of the form rho(R) ~ R^n to the radial density distribution of RR Lyrae in the Galactic halo. The best fit corresponds to the spherical case, for which we obtain a simple power-law index of n=-4.17^{+0.18}_{-0.20}, consistent with recent studies made with samples covering shorter distances. The pulsational properties of the outermost RR Lyrae in the sample (d_H>90 kpc) differ from the ones in the halo population at closer distances. The distribution of the stars in a Period-Amplitude diagram suggest they belong to Oosterhoff-intermediate or Oosterhoff II groups, similar to what is found in the ultra-faint dwarf satellites around the Milky Way. The new distant stars discovered represent an important addition to the few existing tracers of the Milky Way potential in the outer halo.
During the analysis of RR Lyrae stars discovered in the High cadence Transient Survey (HiTS) taken with the Dark Energy Camera at the 4-m telescope at Cerro Tololo Inter-American Observatory, we found a group of three very distant, fundamental mode pulsator RR Lyrae (type ab). The location of these stars agrees with them belonging to the Leo V ultra-faint satellite galaxy, for which no variable stars have been reported to date. The heliocentric distance derived for Leo V based on these stars is 173 +/- 5 kpc. The pulsational properties (amplitudes and periods) of these stars locate them within the locus of the Oosterhoff II group, similar to most other ultra-faint galaxies with known RR Lyrae stars. This serendipitous discovery shows that distant RR Lyrae stars may be used to search for unknown faint stellar systems in the outskirts of the Milky Way.
We present the first results of the High cadence Transient Survey (HiTS), a survey whose objective is to detect and follow up optical transients with characteristic timescales from hours to days, especially the earliest hours of supernova (SN) explosions. HiTS uses the Dark Energy Camera (DECam) and a custom made pipeline for image subtraction, candidate filtering and candidate visualization, which runs in real-time to be able to react rapidly to the new transients. We discuss the survey design, the technical challenges associated with the real-time analysis of these large volumes of data and our first results. In our 2013, 2014 and 2015 campaigns we have detected more than 120 young SN candidates, but we did not find a clear signature from the short-lived SN shock breakouts (SBOs) originating after the core collapse of red supergiant stars, which was the initial science aim of this survey. Using the empirical distribution of limiting-magnitudes from our observational campaigns we measured the expected recovery fraction of randomly injected SN light curves which included SBO optical peaks produced with models from Tominaga et al. (2011) and Nakar & Sari (2010). From this analysis we cannot rule out the models from Tominaga et al. (2011) under any reasonable distributions of progenitor masses, but we can marginally rule out the brighter and longer-lived SBO models from Nakar & Sari (2010) under our best-guess distribution of progenitor masses. Finally, we highlight the implications of this work for future massive datasets produced by astronomical observatories such as LSST.