Spectrum of a uniform grid of strings
type: Item
instance of: scholarly article
title: Spectrum of a uniform grid of strings
zbMATH Open document ID: 0958.35091
author: A. Komarov
author: O. M. Penkin
author: Yu. V. Pokornij
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: The spectrum \(\Lambda \) of a homogeneous membrane, spanned in the unit square, is investigated by approximating it with a network of strings \(\Gamma_h\) of meshsize \(h\). It is shown that for each \(M\) the spectrum \(\Lambda \) in \(|\lambda |\leq M\) differs from the spectrum of \(\Gamma _h\) by \(O(h^2)\). The spectrum of \(\Gamma _h\) is shown to be the set of solutions of explicitly given equations involving trigonometric functions.
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 34B45
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1541608
zbMATH Keywords: network
zbMATH Keywords: homogeneous membrane
zbMATH Keywords: spectrum
zbMATH Keywords: eigenvalue estimates
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1541608