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2005-2006 Eigenvalues associated with Borel sets.
Hans Volkmer
Author Affiliations +
Real Anal. Exchange 31(1): 111-124 (2005-2006).


Every Borel subset $K$ of an interval $[c,d]$ induces a sequence of eigenvalues. If $K$ is closed, the asymptotic behavior of the eigenvalues is related to the positions and lengths of its complementary intervals. The rate of growth becomes ``lowest possible'' if $K$ has self-similarity properties. Eigenvalues of a vibrating string with singular mass distribution are eigenvalues associated with a set $K$.


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Hans Volkmer. "Eigenvalues associated with Borel sets.." Real Anal. Exchange 31 (1) 111 - 124, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1108.34022
MathSciNet: MR2218192

Primary: 34B24
Secondary: 26A30

Keywords: eigenvalue problem , Symmetric Perfect Set , vibrating string

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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