## Real Analysis Exchange

### Eigenvalues associated with Borel sets.

Hans Volkmer

#### 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

https://projecteuclid.org/euclid.rae/1149516812

Mathematical Reviews number (MathSciNet)
MR2218192

Zentralblatt MATH identifier
1108.34022

#### 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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