Displaying similar documents to “Properties of eigenfunctions of non-local operators”

De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation

Libor Báňa, Ondřej Došlý (2014)

Archivum Mathematicum

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We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part...

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

Khelifi, Abdessatar (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 35J05, 35C15, 44P05 In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic...

Eigenvalues of a Linear Transformation

Karol Pąk (2008)

Formalized Mathematics

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The article presents well known facts about eigenvalues of linear transformation of a vector space (see [13]). I formalize main dependencies between eigenvalues and the diagram of the matrix of a linear transformation over a finite-dimensional vector space. Finally, I formalize the subspace [...] called a generalized eigenspace for the eigenvalue λ and show its basic properties.MML identifier: VECTSP11, version: 7.9.03 4.108.1028