Eigenvalues for infinite matrices

Shivakumar, P. N.; Williams, J. J.; Rudraiah, N.

doi:10.1016/0024-3795(87)90335-1

Cited by 46 publications

(43 citation statements)

References 8 publications

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“…l p , for p < 1. An extension of these results was obtained in [20] for p ¼ 1 by introducing column diagonally dominant matrices. In addition, Geršgorin localization theorems for p ¼ 1 and p ¼ 1 were introduced.…”

Section: Introductionmentioning

confidence: 85%

Spectrum localizations for matrix operators on lp spaces

Aleksić

Kostić

Zigic

2014

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 85%

Spectrum localizations for matrix operators on lp spaces

Aleksić

Kostić

Zigic

2014

Applied Mathematics and Computation

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“…There have been several papers studying the localization of eigenvalues for infinite matrices, see for instance Hannani et al [9] and Shivakumar et al [12]. One condition that has been well studied is for a matrix to be diagonally dominant, in which case extensions of the wellknown Gershgorin's theorem can be obtained.…”

Section: Eingenvalues and Eigenvectorsmentioning

confidence: 98%

Eigenvalues and hypercyclicity in omega

Salas

2011

RACSAM

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“…The time-independent Schrödinger equation is an eigenvalue problem for infinite matrices [23][24][25]. The solutions of Equation (20) are considered in [9,10].…”

Section: Exact Discretization Of Quantum Mechanicsmentioning

confidence: 99%

Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

Tarasov

2016

Mathematics

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An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.

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Eigenvalues for infinite matrices

Cited by 46 publications

References 8 publications

Spectrum localizations for matrix operators on lp spaces

Spectrum localizations for matrix operators on lp spaces

Eigenvalues and hypercyclicity in omega

Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

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