Real Analysis Exchange

Eigenvalues associated with Borel sets.

Hans Volkmer

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Abstract

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

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

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516812

Mathematical Reviews number (MathSciNet)
MR2218192

Zentralblatt MATH identifier
1108.34022

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

Keywords
Symmetric perfect set vibrating string eigenvalue problem

Citation

Volkmer, Hans. Eigenvalues associated with Borel sets. Real Anal. Exchange 31 (2005), no. 1, 111--124. https://projecteuclid.org/euclid.rae/1149516812


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References

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