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This article is cited in 4 scientific papers (total in 4 papers)
Spectral properties of operators of the theory of harmonic potential
J. Ahnera, V. V. Dyakinb, V. Ya. Raevskiib, S. Ritterc a Vanderbilt University
b Institute of Metal Physics, Ural Division of the Russian Academy of Sciences
c Universität Karlsruhe
Abstract:
We classify the points of the spectrum of the operators $B$ and $B^*$ of the theory of harmonic potential on a smooth closed surface $S\subset\mathbb R^3$. These operators give the direct value on $S$ of the normal derivative of the simple layer potential and the double layer potential. We show that zero can belong to the point spectrum of both operators in $L_2(S)$. We prove that the half-interval $[-2,2)$ is densely filled by spectrum points of the operators for a varying surface; this is a generalization of the classical result of Plemelj. We obtain a series of new spectral properties of the operators $B$ and $B^*$ on ellipsoidal surfaces.
Received: 13.12.1994
Citation:
J. Ahner, V. V. Dyakin, V. Ya. Raevskii, S. Ritter, “Spectral properties of operators of the theory of harmonic potential”, Mat. Zametki, 59:1 (1996), 3–11; Math. Notes, 59:1 (1996), 3–9
Linking options:
https://www.mathnet.ru/eng/mzm1689https://doi.org/10.4213/mzm1689 https://www.mathnet.ru/eng/mzm/v59/i1/p3
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Abstract page: | 491 | Full-text PDF : | 215 | References: | 83 | First page: | 1 |
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