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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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A Real Analyticity Result for Symmetric Functions of the Eigenvalues of a Domain-Dependent Neumann Problem for the Laplace Operator
TL;DR: In this article, the Neumann eigenvalue problem for the Laplace operator in the open subset of an open connected subset of the Euclidean space is studied. But the authors only consider the case where the Sobolev space W 1,2(Ω) into the space L 2(ϵ) is compact.
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Domain deformations and eigenvalues of the Dirichlet Laplacian in a Riemannian manifold
Ahmad El Soufi,Saïd Ilias +1 more
TL;DR: In this article, the Dirichlet Laplacian of a real analytic Riemannian manifold was considered as a functional domain and necessary and sufficient conditions for a domain to be critical, locally minimizing or locally maximizing.
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Perturbation Theory for Analytic Matrix Functions: The Semisimple Case
TL;DR: New sufficient conditions for analytic dependence of eigenvalue functions, $\lambda(\alpha)$, on $\alpha$ in a neighborhood of $\alpha_0$ are obtained and connections with known results on self-adjoint problems are made.
Book ChapterDOI
Classical Limits of Eigenfunctions for Some Completely Integrable Systems
Dmitry Jakobson,Steve Zelditch +1 more
TL;DR: In this article, it was shown that adding a ψDO of order -n + 2 to the level spacings distribution of Δ on a negatively curved manifold of dimension n does not change the quantum ergodicity.
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Large-Scale Computation of $\mathcal{L}_\infty$-Norms by a Greedy Subspace Method
TL;DR: A subspace projection method is proposed to obtain approximations of the function H where the middle factor is of much smaller dimension and certain Hermite interpolation properties hold between the largest singular values of the original and the reduced function.