Real Analysis Exchange

Eigenvalues associated with Borel sets.

Hans Volkmer

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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 $K$.

Article information

Real Anal. Exchange, Volume 31, Number 1 (2005), 111-124.

First available in Project Euclid: 5 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B24: Sturm-Liouville theory [See also 34Lxx]
Secondary: 26A30: Singular functions, Cantor functions, functions with other special properties

Symmetric perfect set vibrating string eigenvalue problem


Volkmer, Hans. Eigenvalues associated with Borel sets. Real Anal. Exchange 31 (2005), no. 1, 111--124.

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