On the asymptotic distribution of eigenvalues of banded matrices

1988 ◽  
Vol 4 (1) ◽  
pp. 403-417 ◽  
Author(s):  
Jeffrey S. Geronimo ◽  
Evans M. Harrell ◽  
Walter Van Assche
Keyword(s):  
Asymptotic Distribution ◽  
Banded Matrices ◽  
Distribution Of Eigenvalues

scholarly journals Asymptotic Distribution of Eigenvalues of a Constrained Translating String

1997 ◽  
Vol 64 (3) ◽  
pp. 613-619 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote ◽  
B. Z. Guo
Keyword(s):  
Spectral Analysis ◽  
Asymptotic Distribution ◽  
Characteristic Equation ◽  
Infinite Number ◽  
Imaginary Axis ◽  
Irrational Number ◽  
Coupled System ◽  
Numerical Analyses ◽  
Vibration Energy ◽  
Distribution Of Eigenvalues

A new spectral analysis for the asymptotic locations of eigenvalues of a constrained translating string is presented. The constraint modeled by a spring-mass-dashpot is located at any position along the string. Asymptotic solutions for the eigenvalues are determined from the characteristic equation of the coupled system of constraint and string for all constraint parameters. Damping in the constraint dissipates vibration energy in all modes whenever its dimensionless location along the string is an irrational number. It is shown that although all eigenvalues have strictly negative real parts, an infinite number of them approach the imaginary axis. The analytical predictions for the distribution of eigenvalues are validated by numerical analyses.

scholarly journals Interpolation methods to estimate eigenvalue distribution of some integral operators

2004 ◽  
Vol 2004 (9) ◽  
pp. 479-485
Author(s):  
E. M. El-Shobaky ◽  
N. Abdel-Mottaleb ◽  
A. Fathi ◽  
M. Faragallah
Keyword(s):  
Besov Space ◽  
Asymptotic Distribution ◽  
Function Space ◽  
Integral Operators ◽  
Eigenvalue Distribution ◽  
Factorization Theorem ◽  
Lizorkin Space ◽  
Interpolation Methods ◽  
Distribution Of Eigenvalues

We study the asymptotic distribution of eigenvalues of integral operatorsTkdefined by kernelskwhich belong to Triebel-Lizorkin function spaceFpuσ(F  qvτ)by using the factorization theorem and the Weyl numbersxn. We use the relation between Triebel-Lizorkin spaceFpuσ(Ω)and Besov spaceBpqτ(Ω)and the interpolation methods to get an estimation for the distribution of eigenvalues in Lizorkin spacesFpuσ(F  qvτ).

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