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).

scholarly journals On the asymptotic distribution of eigenvalues

1950 ◽  
Vol 200 (1063) ◽  
pp. 572-580 ◽  
Keyword(s):  
Approximate Solution ◽  
Schrödinger Equation ◽  
Asymptotic Distribution ◽  
Schrodinger Equation ◽  
Eigenvalue Distribution ◽  
Three Dimensions ◽  
One Dimension ◽  
One Dimensional ◽  
Distribution Of Eigenvalues ◽  
The One

It is well known that the asymptotic distribution of the eigenvalues of the one-dimensional Schrödinger equation is provided by the so-called W. K. B. formula. Most proofs of this depend on the approximate solution of the equation in two regions and the joining up of these solutions at the boundaries of the regions in a certain way. These methods are not easily generalized to the Schrödinger equation for dimensions greater than one. In the present paper the methods of Courant & Hilbert are applied to this problem and they lead very simply to a proof of the known result in one dimension and to analogous formulae for the eigenvalue distribution of the Schrödinger equation in two and three dimensions.

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
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