Spectral analysis and spectral synthesis on discrete Abelian groups

2007 ◽  
pp. 25-48
Author(s):  
László Székelyhidi
Keyword(s):  
Spectral Analysis ◽  
Abelian Groups ◽  
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.

On spectral synthesis on zero-dimensional Abelian groups

2013 ◽  
Vol 204 (9) ◽  
pp. 1332-1346 ◽  
Author(s):  
S S Platonov
Keyword(s):  
Abelian Groups ◽  
Spectral Synthesis

scholarly journals Spectral synthesis on discrete Abelian groups

2007 ◽  
Vol 143 (1) ◽  
pp. 103-120 ◽  
Author(s):  
M. LACZKOVICH ◽  
L. SZÉKELYHIDI
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Spectral Synthesis ◽  
Free Rank ◽  
Discrete Abelian Group ◽  
Torsion Free Rank ◽  
Torsion Free

AbstractWe prove that spectral synthesis holds on a discrete Abelian group G if and only if the torsion free rank of G is finite.

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.

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