Principles of finite-dimensional perturbation theory

1997 ◽  
Vol 23 (1) ◽  
pp. 59-68 ◽  
Author(s):  
I. V. Krasovskiı̆ ◽  
V. I. Peresada
Keyword(s):  
Perturbation Theory ◽  
Finite Dimensional ◽  
Dimensional Perturbation Theory

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]).

Perturbation Theory for Weak Measurements in Quantum Mechanics, Systems with Finite-Dimensional State Space

2018 ◽  
Vol 20 (1) ◽  
pp. 299-335 ◽  
Author(s):  
Miguel Ballesteros ◽  
Nick Crawford ◽  
Martin Fraas ◽  
Jürg Fröhlich ◽  
Baptiste Schubnel
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
State Space ◽  
Weak Measurements ◽  
Finite Dimensional ◽  
Dimensional State Space

scholarly journals Dimensional perturbation theory on the Connection Machine

1994 ◽  
Vol 8 (6) ◽  
pp. 712 ◽  
Author(s):  
Timothy C. Germann ◽  
Dudley R. Herschbach ◽  
Bruce M. Boghosian
Keyword(s):  
Perturbation Theory ◽  
Connection Machine ◽  
Dimensional Perturbation Theory
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