Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wires

2008 ◽  
Vol 387 (19-20) ◽  
pp. 4733-4739 ◽  
Author(s):  
O.V. Usatenko ◽  
S.S. Melnik ◽  
L. Kroon ◽  
M. Johansson ◽  
R. Riklund ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Long Range ◽  
Quantum Wires ◽  
Diffraction Gratings ◽  
Correlated Systems ◽  
Analysis And Synthesis ◽  
Spectral Analysis And 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.

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