On the spectral properties of the matrix-valued Friedrichs model

1991 ◽  
pp. 1-38 ◽  
Author(s):  
Zh. Abdullaev ◽  
S. Lakaev
Keyword(s):  
Spectral Properties ◽  
The Matrix ◽  
Friedrichs Model

Some spectral properties of the generalized Friedrichs model

1989 ◽  
Vol 45 (6) ◽  
pp. 1540-1563 ◽  
Author(s):  
S. N. Lakaev
Keyword(s):  
Spectral Properties ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

scholarly journals SOME SPECTRAL PROPERTIES OF THE NON-SELF-ADJOINT FRIEDRICHS MODEL OPERATOR

2005 ◽  
Vol 105A (2) ◽  
pp. 25-46
Author(s):  
Alexander V. Kiselev
Keyword(s):  
Spectral Properties ◽  
Model Operator ◽  
Friedrichs Model

SPECTRAL PROPERTIES OF ADMITTANCE MATRICES OF RESISTIVE TREE NETWORKS

1994 ◽  
Vol 04 (01) ◽  
pp. 53-70
Author(s):  
I. CEDERBAUM
Keyword(s):  
Characteristic Frequency ◽  
Spectral Properties ◽  
Rational Functions ◽  
Resistive Network ◽  
Admittance Matrix ◽  
Sturm Sequences ◽  
Classical Work ◽  
Mechanical Analogue ◽  
The Matrix ◽  
General Tree

In this paper spectral properties of the admittance matrix of a resistive network whose underlying graph forms a general tree are studied. The algebraic presentation of the network is provided by its real node admittance matrix with respect to one of its terminal vertices, considered to be the root of the tree. The spectral properties of this matrix are studied by application of the theory of two-element-kind (R, C) networks. A mechanical analogue of a particular case of a similar problem, corresponding to a linear tree has been studied in the classical work of Gantmacher and Krein.7 Generalization of the study to networks based on trees of arbitrary structure calls for a modification of the mathematical approach. Instead of polynomial Sturm sequences applied in Ref. 7 the paper applies sequences of rational functions obeying the two basic Sturm conditions. In the special case of a linear tree these rational functions turn out to be polynomials, and the results are equivalent to those in Ref. 7. For a general tree the paper takes into consideration any root—leaf path of the tree. It is shown that the conditions on such a path are similar to those taking place on a linear tree. Some difference occurs in the number of sign reversals in the sequence of coordinates of characteristic vectors. In the case of a linear tree this number depends only on the position of the corresponding characteristic frequency in the spectrum of the matrix. In the case of a root-leaf path of a general tree, this number has to be normally decreased. The correction (which might be zero) is equal to the number of poles of the determinant of the reduced admittance matrix corresponding to the path considered, which does not exceed the characteristic frequency.

Jost solution and the spectral properties of the matrix-valued difference operators

2012 ◽  
Vol 218 (19) ◽  
pp. 9676-9681 ◽  
Author(s):  
Yelda Aygar ◽  
Elgiz Bairamov
Keyword(s):  
Spectral Properties ◽  
Difference Operators ◽  
The Matrix ◽  
Jost Solution

scholarly journals Fractional Laplace operator in two dimensions, approximating matrices, and related spectral analysis

CALCOLO ◽  
2020 ◽  
Vol 57 (3) ◽  
Author(s):  
Lidia Aceto ◽  
Mariarosa Mazza ◽  
Stefano Serra-Capizzano
Keyword(s):  
Spectral Analysis ◽  
Laplace Operator ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Two Dimensions ◽  
Spatial Variables ◽  
The Matrix ◽  
Constant Coefficients ◽  
Fractional Laplace Operator ◽  
Concise Description

Abstract In this work we review some proposals to define the fractional Laplace operator in two or more spatial variables and we provide their approximations using finite differences or the so-called Matrix Transfer Technique. We study the structure of the resulting large matrices from the spectral viewpoint. In particular, by considering the matrix-sequences involved, we analyze the extreme eigenvalues, we give estimates on conditioning, and we study the spectral distribution in the Weyl sense using the tools of the theory of Generalized Locally Toeplitz matrix-sequences. Furthermore, we give a concise description of the spectral properties when non-constant coefficients come into play. Several numerical experiments are reported and critically discussed.

Spectral properties of the generalized Friedrichs model

2010 ◽  
Vol 163 (1) ◽  
pp. 414-428 ◽  
Author(s):  
E. R. Akchurin
Keyword(s):  
Spectral Properties ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model
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