3 Spectral Analysis of Finite Dimensional Operators

2006 ◽  
pp. 13-17
Author(s):  
Christian A. Schenk ◽  
Gerhart I. Schuëller
Keyword(s):  
Spectral Analysis ◽  
Finite Dimensional

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.

scholarly journals Multi-variable quaternionic spectral analysis

2021 ◽  
Vol 41 (3) ◽  
pp. 335-379
Author(s):  
Ilwoo Cho ◽  
Palle E.T. Jorgensen
Keyword(s):  
Spectral Analysis ◽  
Functional Equations ◽  
Linear Functional ◽  
Vector Spaces ◽  
Complex Numbers ◽  
Dimensional Vector ◽  
Finite Dimensional ◽  
Linear Functional Equations ◽  
Non Linear

In this paper, we consider finite dimensional vector spaces \(\mathbb{H}^n\) over the ring \(\mathbb{H}\) of all quaternions. In particular, we are interested in certain functions acting on \(\mathbb{H}^n\), and corresponding functional equations. Our main results show that (i) all quaternions of \(\mathbb{H}\) are classified by the spectra of their realizations under representation, (ii) all vectors of \(\mathbb{H}^n\) are classified by a canonical extended setting of (i), and (iii) the usual spectral analysis on the matricial ring \(M_n(\mathbb{C})\) of all \((n \times n)\)-matrices over the complex numbers \(\mathbb{C}\) has close connections with certain "non-linear" functional equations on \(\mathbb{H}^n\) up to the classification of (ii).

Spectral analysis of asymmetry training effect for depression

2008 ◽  
Author(s):  
Ji Ha Lee ◽  
Sung Won Choi ◽  
Ji Sun Min ◽  
Eun Ju Jaekal ◽  
Gyhye Sung
Keyword(s):  
Spectral Analysis ◽  
Training Effect

Some problems in the spectral analysis of human behavior records

1953 ◽  
Author(s):  
C. J. Burke ◽  
R. Narasimhan ◽  
O. J. Benepe
Keyword(s):  
Spectral Analysis ◽  
Human Behavior
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