On the Perturbed Eigenvalue Problem
Copyright policy )On the Perturbed Eigenvalue Problem
The author considers the perturbed eigenvalue problem \(L(x) v(x)= \lambda(x) v(x)\) near \(0= x\in \mathbb{R}\) with \(L(x)\) a Fredholm operator of index zero. Using the implicit function theorem and the bordering lemma, he derives a necessary and sufficient smoothness condition for the characteristic pairs \((\lambda(x), v(x))\) with eigenvalue \(\lambda(x)\) emanating from a semi-simple eigenvalue \(\lambda(0)\) of \(L(0)\).
- University of Stuttgart Germany
Perturbation theory of linear operators, bordering lemma, implicit function theorem, Applied Mathematics, Eigenvalue problems for linear operators, Fredholm operator of index zero, perturbed eigenvalue problem, Analysis
Perturbation theory of linear operators, bordering lemma, implicit function theorem, Applied Mathematics, Eigenvalue problems for linear operators, Fredholm operator of index zero, perturbed eigenvalue problem, Analysis
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