On the principal ideal theorem and spectral synthesis on discrete Abelian groups

2016 ◽  
Vol 150 (1) ◽  
pp. 228-233 ◽  
Author(s):  
L. Székelyhidi
Keyword(s):  
Principal Ideal ◽  
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.

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.

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