|
Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2013, Volume 15, Number 3, Pages 100–107
(Mi svmo403)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
In Middle Volga Mathematical Society
Comments to the problems of small perturbations of linear
equations and linear term of the spectral characteristics of a Fredholm
operator
A. A. kjashkina, B. V. Loginovb, P. A. Shamanaeva a Ogarev Mordovia State University
b Ulyanovsk State Technical University
Abstract:
In the monograph [1] and the article [1,2]
the problem on perturbation of linear equation by small linear summand
of the form $(B-\varepsilon A)x=h$ were investigated with closely
defined on $D_{B}$ Fredholmian operator $B:E_{1}\supset D_{B}\rightarrow E_{2}$,
$D_{A}\supset D_{B}$, or $A\in L\{E_{1},E_{2}\}$, $\varepsilon\in\mathbb{C}^{1}$
- small parameter, $E_{1}$ and $E_{2}$ - are Banach spaces. The
application of the results [3,4] formulated
in the form of the lemma on the biorthogonality of generalized Jordan
chains allows to give some retainings of the results [1,2].
This problem is considered here in the general case of sufficiently
smooth (analytic) by $\varepsilon$ operator-function $A(\varepsilon)$.
It is given also the application of the biorthogonality lemma and
branching equation in the root subspaces to the problem on perturbation
of Fredholm points in $C$-spectrum of the operator $A(0)$.
Keywords:
linear
operators in Banach spaces, perturbation theory.
Linking options:
https://www.mathnet.ru/eng/svmo403
|
Statistics & downloads: |
Abstract page: | 62 | References: | 12 |
|