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Keywords
(2)
Linear Operator
Perturbation Theory
Related Publications
(177)
Methods of Modern Mathematical Physics
Methods of modern mathematical physics I: functional analysis
Maximal Operators Associated with Dirichlet Forms Perturbed by Measures
Methods of modern mathematical physics
Methods of modern mathematical physics IV: Analysis of operators
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Perturbation theory for linear operators
Perturbation theory for linear operators,T. Kato
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Perturbation theory for linear operators
(
Citations: 5221
)
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T. Kato
Published in 1980.
Cumulative
Annual
Citation Context
(2014)
...[
16
][Problem V4...
F. Bentosela
,
et al.
On the Guided States of 3D Biperiodic Schrödinger Operators
...It is clear to see that By the results of Kato
16
, we have It suffices to show the dependence of
Gaihui Guo
,
et al.
Bifurcation from a double eigenvalue in the unstirred chemostat
...First, by using results of perturbation theory for linear operators
22
, in <0002S2002">Section 3...
Shuichi Jimbo
,
et al.
A nondestructive method for damage detection in steelconcrete struct...
...Operator
LQ
^{−1}
is welldefined on
X
and one has since operator
Q
^{−1}
commutes with in virtue of our assumption (<0007" reftype="dispformula">7), we deduce that
Q
^{−1}
commutes with Π
^{−1}
12
, p...
Mustapha Cheggag
,
et al.
Abstract differential equations of elliptic type with general Robin bo...
...Then all the eigenvalues (λ
_{ i }
)
_{ i≥1}
of
A
are reals and we have only finitely many eigenvalues (λ
_{ i }
)
_{1≤i≤N }
such that λ
_{ i }
≥ −η for some η > 0, each with finitedimensional eigenspace (Triggiani
1975
; Kato
1980
), and hence the state space
H
can be decomposed according to where
H
_{ u }
= Vect(ϕ
_{ i }
, 1 ≤
i
≤
N
) and
H
_{ s }
= Vect(ϕ
_{ i }
,
i
>
N
) and for all
i
≥ 1, ϕ
_{ i }
is an eigenvector associated to the eigenvalue λ
_{ i }
and we have where
S
_{ s }
(
t
) denotes the restriction of the semigroup
S
(
t
) in
H
_{ s }
...
R. El Ayadi
,
et al.
Strong stabilisation and decay estimate for unbounded bilinear systems
Sort by:
Citations
(5221)
On the Guided States of 3D Biperiodic Schrödinger Operators
F. Bentosela
,
C. Bourrely
,
Y. Dermenjian
,
E. Soccorsi
Journal:
Communications in Partial Differential Equations  COMMUN PART DIFF EQUAT
, vol. justaccep, no. justaccep, 2012
Bifurcation from a double eigenvalue in the unstirred chemostat
Gaihui Guo
,
Jianhua Wu
,
Yane Wang
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 113, 2012
A nondestructive method for damage detection in steelconcrete structures based on finite eigendata
Shuichi Jimbo
,
Antonino Morassi
,
Gen Nakamura
,
Kenji Shirota
Journal:
Inverse Problems in Science and Engineering  INVERSE PROBL SCI ENG
, vol. 20, no. 2, pp. 233270, 2012
Abstract differential equations of elliptic type with general Robin boundary conditions in Hölder spaces
Mustapha Cheggag
,
Angelo Favini
,
Rabah Labbas
,
Stéphane Maingot
,
Ahmed Medeghri
Journal:
Applicable Analysis
, vol. 91, no. 8, pp. 14531475, 2012
Strong stabilisation and decay estimate for unbounded bilinear systems
R. El Ayadi
,
M. Ouzahra
,
A. Boutoulout
Journal:
International Journal of Control  INT J CONTR
, vol. aheadofp, no. aheadofp, pp. 19, 2012