scholarly journals Group interpretation of the spectral parameter. The case of isothermic surfaces

2017 ◽  
Vol 113 ◽  
pp. 28-37
Author(s):  
Jan L. Cieśliński ◽  
Artur Kobus
Keyword(s):  
Spectral Parameter ◽  
Isothermic Surfaces

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]).

scholarly journals On the Spectral Parameter Problem

2009 ◽  
Vol 109 (1) ◽  
pp. 239-255 ◽  
Author(s):  
Michal Marvan
Keyword(s):  
Spectral Parameter ◽  
Parameter Problem

scholarly journals Homogenization of the spectral problem on the Riemannian manifold consisting of two domains connected by many tubes

2013 ◽  
Vol 143 (6) ◽  
pp. 1255-1289 ◽  
Author(s):  
Andrii Khrabustovskyi
Keyword(s):  
Riemannian Manifold ◽  
Small Parameter ◽  
Asymptotic Behaviour ◽  
Spectral Problem ◽  
Spectral Parameter ◽  
Beltrami Operator ◽  
Perforated Domain ◽  
Perforated Domains ◽  
Accumulation Points ◽  
Image Position

The paper deals with the asymptotic behaviour as ε → 0 of the spectrum of the Laplace–Beltrami operator Δε on the Riemannian manifold Mε (dim Mε = N ≥ 2) depending on a small parameter ε > 0. Mε consists of two perforated domains, which are connected by an array of tubes of length qε. Each perforated domain is obtained by removing from the fixed domain Ω ⊂ ℝN the system of ε-periodically distributed balls of radius dε = ō(ε). We obtain a variety of homogenized spectral problems in Ω; their type depends on some relations between ε, dε and qε. In particular, if the limitsare positive, then the homogenized spectral problem contains the spectral parameter in a nonlinear manner, and its spectrum has a sequence of accumulation points.

scholarly journals Quantum dynamical -matrix with spectral parameter from fusion

1998 ◽  
Vol 31 (42) ◽  
pp. 8533-8538
Author(s):  
Xu-Dong Luo ◽  
Xing-Chang Song ◽  
Shi-Kun Wang ◽  
Ke Wu
Keyword(s):  
Spectral Parameter ◽  
Dynamical Matrix ◽  
Quantum Dynamical
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