Displaying similar documents to “Symmetric subspaces related to certain eigenvalue problems”

A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

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The operator L 0 : D L 0 ⊂ H → H , L 0 u = 1 r d d r r d d r 1 r d d r r d u d r , D L 0 = { u ∈ C 4 ( [ 0 , R ] ) , u ' ( 0 ) = u ' ' ' ' ( 0 ) = 0 , u ( R ) = u ' ( R ) = 0 } , H = L 2 , r ( 0 , R ) is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on L 0 (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types L 0 u = g and u t t + L 0 u = g , respectively.

Proper subspaces and compatibility

Esteban Andruchow, Eduardo Chiumiento, María Eugenia Di Iorio y Lucero (2015)

Studia Mathematica

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Let 𝓔 be a Banach space contained in a Hilbert space 𝓛. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambickiĭ, we say that a bounded operator on 𝓔 is a proper operator if it admits an adjoint with respect to the inner product of 𝓛. A proper operator which is self-adjoint with respect to the inner product of 𝓛 is called symmetrizable. By a proper subspace 𝓢 we mean a closed subspace of 𝓔 which is the range of a proper projection....

Spectral approximation of positive operators by iteration subspace method

Andrzej Pokrzywa (1984)

Aplikace matematiky

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The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators A n arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators A n is also considered.