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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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Approximate Normal Forms via Floquet–Bloch Theory: Nehorošev Stability for Linear Waves in Quasiperiodic Media
TL;DR: In this article, an approximate stationary Floquet-Bloch theory is used to put the perturbed Schrodinger operator into approximate normal form, which leads to an accurate long-time description of the Schodoringer flow as an effective unitary correction of the free flow.
Shape sensitivity analysis of the eigenvalues of polyharmonic operators and elliptic systems
TL;DR: In this paper, the authors studied the dependence of the eigenvalues of elliptic partial differential operators upon domain perturbations in the N-dimensional space and obtained Hadamard-type formulas which were used to provide a characterization of critical domains under volume constraint.
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The Generalized Davies Problem for Polyharmonic Operators
TL;DR: In this paper, the Davies problem is connected with the maximal constants in Hardy-type inequalities for polyharmonic operators in domains of the Euclidean space, and the generalizations of this problem to the Rellich type inequalities are studied under an additional minimal condition on the boundary of the domain.
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Eigenvalues of the sub-Laplacian and deformations of contact structures on a compact CR manifold
TL;DR: In this article, the authors studied the differentiability of the eigenvalues of the sub-Laplacian Δ b, θ associated with a compatible contact form (i.e., a pseudo-Hermitian structure) under conformal deformations of θ.