Spectral synthesis and spectral analysis

2007 ◽  
pp. 7-23
Author(s):  
László Székelyhidi
Keyword(s):  
Spectral Analysis ◽  
Spectral Synthesis

Spectral synthesis and residually finite-dimensional algebras

2017 ◽  
Vol 16 (10) ◽  
pp. 1750200 ◽  
Author(s):  
László Székelyhidi ◽  
Bettina Wilkens
Keyword(s):  
Spectral Analysis ◽  
Abelian Group ◽  
Theoretical Approach ◽  
Abelian Groups ◽  
Spectral Synthesis ◽  
Residually Finite ◽  
Finite Dimensional ◽  
Analysis And Synthesis ◽  
Spectral Analysis And Synthesis

In 2004, a counterexample was given for a 1965 result of R. J. Elliott claiming that discrete spectral synthesis holds on every Abelian group. Since then the investigation of discrete spectral analysis and synthesis has gained traction. Characterizations of the Abelian groups that possess spectral analysis and spectral synthesis, respectively, were published in 2005. A characterization of the varieties on discrete Abelian groups enjoying spectral synthesis is still missing. We present a ring theoretical approach to the issue. In particular, we provide a generalization of the Principal Ideal Theorem on discrete Abelian groups.

Stellar parameters with FASMA: a new spectral synthesis package

2017 ◽  
Vol 12 (S330) ◽  
pp. 271-272
Author(s):  
M. Tsantaki ◽  
D. T. Andreasen ◽  
G. D. C. Teixeira ◽  
S. G. Sousa ◽  
N. C. Santos ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Spectral Synthesis ◽  
Computational Time ◽  
Spectral Information ◽  
Atmospheric Parameters ◽  
Chemical Abundances ◽  
Analysis Techniques ◽  
Medium Resolution ◽  
Similar Accuracy ◽  
Temperature Surface

AbstractCurrent Galactic surveys, including the Gaia mission, rely on the efficiency of the spectral analysis techniques to provide precise and accurate spectral information (i.e. effective temperature, surface gravity, metallicity, and chemical abundances) in the shortest computational time. In this work, we present a new package to preform complete spectral analyses based on the spectral synthesis technique (Tsantaki et al. 2017, submitted). We focus on deriving atmospheric parameters for FGK-type stars using both high and medium resolution (GIRAFFE) spectra. This method is implemented on the Gaia-ESO benchmark stars to confirm its validity, achieving similar accuracy for the two resolution setups.

scholarly journals Vector valued mean-periodic functions on groups

2002 ◽  
Vol 72 (3) ◽  
pp. 363-388 ◽  
Author(s):  
P. Devaraj ◽  
Inder K. Rana
Keyword(s):  
Banach Space ◽  
Spectral Analysis ◽  
Spectral Synthesis ◽  
Complex Banach Space ◽  
Continuous Functions ◽  
Compact Sets ◽  
Periodic Functions ◽  
Finite Variation ◽  
Locally Compact ◽  
Vector Valued

AbstractLet G be a locally compact Hausdorif abelian group and X be a complex Banach space. Let C(G, X) denote the space of all continuous functions f: G → X, with the topology of uniform convergence on compact sets. Let X′ denote the dual of X with the weak* topology. Let Mc(G, X′) denote the space of all X′-valued compactly supported regular measures of finite variation on G. For a function f ∈ C(G, X) and μ ∈ Mc(G, X′), we define the notion of convolution f * μ. A function f ∈ C(G, X) is called mean-periodic if there exists a non-trivial measure μ ∈ Mc(G, X′) such that f * μ = 0. For μ ∈ Mc(G, X′), let M P(μ) = {f ∈ C(G, X): f * μ = 0} and let M P(G, X) = ∪μ M P(μ). In this paper we analyse the following questions: Is M P(G, X) ≠ 0? Is M P(G, X) ≠ C(G, X)? Is M P(G, X) dense in C(G, X)? Is M P(μ) generated by ‘exponential monomials’ in it? We answer these questions for the groups G = ℝ, the real line, and G = T, the circle group. Problems of spectral analysis and spectral synthesis for C(ℝ, X) and C(T, X) are also analysed.

scholarly journals PEPSI deep spectra

2018 ◽  
Vol 612 ◽  
pp. A46 ◽  
Author(s):  
C. E. Mack ◽  
K. G. Strassmeier ◽  
I. Ilyin ◽  
S. C. Schuler ◽  
F. Spada ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
High Resolution ◽  
Mass Fraction ◽  
Spectral Synthesis ◽  
Bulk Composition ◽  
Spectral Lines ◽  
Elemental Abundance ◽  
Condensation Temperature ◽  
Core Mass ◽  
Rocky Planets

Context. With the Large Binocular Telescope (LBT), we obtained a spectrum with PEPSI, its new optical high-resolution échelle spectrograph. The spectrum has very high resolution and a high signal-to-noise (S/N) and is of the K0V host Kepler−444, which is known to host five sub-Earth-sized rocky planets. The spectrum has a resolution of R ≈ 250 000, a continuous wavelength coverage from 4230 Å to 9120 Å, and an S/N between 150–550:1 (blue to red). Aim. We performed a detailed chemical analysis to determine the photospheric abundances of 18 chemical elements. These were used to place constraints on the bulk composition of the five rocky planets. Methods. Our spectral analysis employs the equivalent-width method for most of our spectral lines, but we used spectral synthesis to fit a small number of lines that required special care. In both cases, we derived our abundances using the MOOG spectral analysis package and Kurucz model atmospheres. Results. We find no correlation between elemental abundance and condensation temperature among the refractory elements (TC > 950 K). In addition, using our spectroscopic stellar parameters and isochrone fitting, we find an age of 10 ± 1.5 Gyr, which is consistent with the asteroseismic age of 11 ± 1 Gyr. Finally, from the photospheric abundances of Mg, Si, and Fe, we estimate that the typical Fe-core mass fraction for the rocky planets in the Kepler−444 system is approximately 24%. Conclusions. If our estimate of the Fe-core mass fraction is confirmed by more detailed modeling of the disk chemistry and simulations of planet formation and evolution in the Kepler−444 system, then this would suggest that rocky planets in more metal-poor and α-enhanced systems may tend to be less dense than their counterparts of comparable size in more metal-rich systems.

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