Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Analysis of the BATSE Continuous MER data

The CGRO/BATSE database includes many types of data such as the 16-channel continuous background or medium energy resolution burst data (CONT and MER data types). We have calculated some four hundred burst's medium energy resolution spectra and Principal Component Analysis has been applied. We found five components can describe GRBs' spectra.Comment: 4 pages, 2 figures, accepted in Nuovo Ciment

Comparing the observed properties of the GRBs detected by the Fermi and Swift satellites

We studied the distribution of the GRBs, observed by the Fermi satellite, in the multidimensional parameter space consisting of the duration, Fluence, Peak flux and Peak energy (if it was available). About 10% of the Fermi bursts was observed also by the Swift satellite. We did not find significant differences between the Peak flux and Peak energy of GRBs observed and not observed also by the Swift satellite. In contrast, those GRBs detected also by the Swift satellite had significantly greater Fluence and duration. We did a similar study for the GRBs detected by the Swift satellite. About 30% percent of these bursts was also measured by the Fermi satellite. We found a significant difference in the Fluence, Peak flux and Photon index but none in duration. These differences may be accounted for the different construction and observing strategy of the Fermi and Swift satellites.Comment: 7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 5 in eConf Proceedings C130414

Survival analysis of the optical brightness of GRB host galaxies

We studied the unbiased optical brightness distribution which was calculated from the survival analysis of host galaxies and its relationship with the Swift GRB data of the host galaxies observed by the Keck telescopes. Based on the sample obtained from merging the Swift GRB table and the Keck optical data we also studied the dependence of this distribution on the data of the GRBs. Finally, we compared the HGs distribution with standard galaxies distribution which is in the DEEP2 galaxies catalog.Comment: Swift: 10 Years of Discovery. Conference paper. 2-5 December 2014. La Sapienza University, Rome, Ital

Properties of the intermediate type of gamma-ray bursts

Gamma-ray bursts can be divided into three groups ("short", "intermediate", "long") with respect to their durations. The third type of gamma-ray bursts - as known - has the intermediate duration. We show that the intermediate group is the softest one. An anticorrelation between the hardness and the duration is found for this subclass in contrast to the short and long groups.Comment: In Sixteenth Maryland Astrophysics Conferenc

A Principal Component Analysis of the 3B Gamma-Ray Burst Data

We have carried out a principal component analysis for 625 gamma-ray bursts in the BATSE 3B catalog for which non-zero values exist for the nine measured variables. This shows that only two out of the three basic quantities of duration, peak flux and fluence are independent, even if this relation is strongly affected by instrumental effects, and these two account for 91.6% of the total information content. The next most important variable is the fluence in the fourth energy channel (at energies above 320 keV). This has a larger variance and is less correlated with the fluences in the remaining three channels than the latter correlate among themselves. Thus a separate consideration of the fourth channel, and increased attention on the related hardness ratio $H43$ appears useful for future studies. The analysis gives the weights for the individual measurements needed to define a single duration, peak flux and fluence. It also shows that, in logarithmic variables, the hardness ratio $H32$ is significantly correlated with peak flux, while $H43$ is significantly anticorrelated with peak flux. The principal component analysis provides a potentially useful tool for estimating the improvement in information content to be achieved by considering alternative variables or performing various corrections on available measurementsComment: Ap.J., accepted 12/9/97; revised version contains a new appendix, somewhat expanded discussion; latex, aaspp4, 15 page