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Spectral properties of operators of the theory of harmonic potential

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Abstract

We classify the points of the spectrum of the operatorsB andB * of the theory of harmonic potential on a smooth closed surfaceS ⊂ ℝ3. These operators give the direct value onS 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 inL 2 (S). We prove that the half-interval [−2π, 2π) 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 operatorsB andB * on ellipsoidal surfaces.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    J. F. Ahner

  2. Institute for Physics of Metals, Ekaterinburg

    V. V. Dyakin & V. Ya. Raevskii

  3. Mathematishes Institut II, Universität Karlsruhe, Karlsruhe, Germany

    St. Ritter

Authors
  1. J. F. Ahner
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  2. V. V. Dyakin
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  3. V. Ya. Raevskii
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  4. St. Ritter
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Additional information

Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 3–11, January, 1996.

This research was partially supported by the Russian Foundation for Basic Research.

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Ahner, J.F., Dyakin, V.V., Raevskii, V.Y. et al. Spectral properties of operators of the theory of harmonic potential. Math Notes 59, 3–9 (1996). https://doi.org/10.1007/BF02312459

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