scholarly journals On the perturbation theory of closed linear operators.

1952 ◽  
Vol 4 (3-4) ◽  
pp. 323-337 ◽  
Author(s):  
Tosio KATO
Keyword(s):  
Perturbation Theory ◽  
Linear Operators ◽  
Closed Linear Operators

Global Perturbation of Nonlinear Eigenvalues

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián López-Gómez ◽  
Juan Carlos Sampedro
Keyword(s):  
Perturbation Theory ◽  
Spectral Parameter ◽  
Classical Theory ◽  
General Setting ◽  
Perturbation Parameter ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Index Zero ◽  
Finite Dimensional ◽  
Nonlinear Eigenvalues

Abstract This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ⁢ ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ⁢ ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ⁢ ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

Spectral value sets of closed linear operators

2000 ◽  
Vol 456 (1998) ◽  
pp. 1397-1418 ◽  
Author(s):  
E. Gallestey ◽  
D. Hinrichsen ◽  
A. J. Pritchard
Keyword(s):  
Linear Operators ◽  
Value Sets ◽  
Closed Linear Operators

One method for the boundary value problem eigenvalues calcuating for a second-order differential equation with a fractional derivative

2019 ◽  
Vol 10 (01) ◽  
pp. 1941004
Author(s):  
Temirkhan Aleroev ◽  
Hedi Aleroeva ◽  
Lyudmila Kirianova
Keyword(s):  
Differential Equation ◽  
Perturbation Theory ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Linear Operators

In this paper, we give a formula for computing the eigenvalues of the Dirichlet problem for a differential equation of second-order with fractional derivatives in the lower terms. We obtained this formula using the perturbation theory for linear operators. Using this formula we can write out the system of eigenvalues for the problem under consideration.

scholarly journals On Stable Perturbations of the Generalized Drazin Inverses of Closed Linear Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Qianglian Huang ◽  
Lanping Zhu ◽  
Xiaoru Chen ◽  
Chang Zhang
Keyword(s):  
Banach Spaces ◽  
Null Space ◽  
Linear Operators ◽  
Special Cases ◽  
Stable Perturbation ◽  
Closed Linear Operators

We investigate the stable perturbation of the generalized Drazin inverses of closed linear operators in Banach spaces and obtain some new characterizations for the generalized Drazin inverses to have prescribed range and null space. As special cases of our results, we recover the perturbation theorems of Wei and Wang, Castro and Koliha, Rakocevic and Wei, Castro and Koliha and Wei.

scholarly journals Effective high-temperature estimates for intermittent maps

2017 ◽  
Vol 39 (8) ◽  
pp. 2159-2175
Author(s):  
BENOÎT R. KLOECKNER
Keyword(s):  
Perturbation Theory ◽  
High Temperature ◽  
Limit Theorem ◽  
Spectral Gap ◽  
Lipschitz Constant ◽  
Transfer Operator ◽  
Linear Operators ◽  
Suitable Assumption ◽  
Unimodal Map ◽  
Definition Of

Using quantitative perturbation theory for linear operators, we prove a spectral gap for transfer operators of various families of intermittent maps with almost constant potentials (‘high-temperature’ regime). Hölder and bounded $p$-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau–Manneville map, any potential with Lipschitz constant less than 0.0014 has a transfer operator acting on $\operatorname{Lip}([0,1])$ with a spectral gap; and that for any two-to-one unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on $\operatorname{BV}([0,1])$ with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in Giulietti et al [The calculus of thermodynamical formalism. J. Eur. Math. Soc., to appear. Preprint, 2015, arXiv:1508.01297], allowing all results there to be applied under the high-temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.

A Note on the Adjoint of the Product of Operators

1970 ◽  
Vol 13 (1) ◽  
pp. 39-45
Author(s):  
Chia-Shiang Lin
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Closed Subspace ◽  
Linear Operators ◽  
Finite Codimension ◽  
Restricted Condition ◽  
Closed Linear Operators

Cordes and Labrousse ([2] p. 697), and Kaniel and Schechter ([6] p. 429) showed that if S and T are domain-dense closed linear operators on a Hilbert space H into itself, the range of S is closed in H and the codimension of the range of S is finite, then, (TS)* = S*T*. With a somewhat different approach and more restricted condition on S, the same assertion was obtained by Holland [5] recently, that S is a bounded everywhere-defined linear operator whose range is a closed subspace of finite codimension in H.

scholarly journals Multiparameter perturbation theory of matrices and linear operators

2020 ◽  
Vol 373 (4) ◽  
pp. 2933-2948
Author(s):  
Adam Parusiński ◽  
Guillaume Rond
Keyword(s):  
Perturbation Theory ◽  
Linear Operators
Sign in / Sign up

Export Citation Format

Share Document