Asymptotics of eigenvalues of high-order differential operator with discrete self-similar weight
arXiv:1009.5335
Abstract
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.
12 pages, 3 tables