Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight

Details Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight

2010-09-27

arxiv.org/abs/1009.5335v1

Mathematics

Spectral Theory

12 pages, 3 tables

Scientific paper

The spectral problem for the high order differential operator with singular
weight is considered. If the weight is a generalized derivative of self-similar
function with zero spectral degree the asymptotics of eigenvalues is obtained.
They are proved to have exponential growth and depend on the order of
differential operator and self-similarity parameters.

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