TY  - THES
AB  - We study the eigenvalues of the Laplacian Δ µ . Here, µ is a singular measure on a bounded interval with an irregular recursive structure, which include self-similar measures as a special case. The structure can also be randomly build. For this operator we determine the asymptotic growth behaviour of the eigenvalue counting function. Furthermore, in the case where µ is self-similar, we give a representation of the eigenvalues of Δ µ as zero points of generalized sine functions allowing, in particular, an explicit computation. Moreover, we use these functions to describe certain properties of the eigenfunctions.
AU  - Arzt, Peter
DA  - 2014
KW  - Eigenwert
KW  - Eigenvalue
KW  - Laplacian
KW  - fractal
KW  - asymptotic growth
KW  - eigenfunction
LA  - eng
PY  - 2014
TI  - Eigenvalues of measure theoretic Laplacians on Cantor-like sets
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:467-8191
Y2  - 2024-11-22T05:50:02
ER  -