Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
1.1 MATHEMATICS
Abstract
We investigate the problem of similarity to a self-adjoint operator for $J$-positive Sturm-Liouville operators $L=\frac{1}{\omega}(-\frac{d^2}{dx^2}+q)$ with $2\pi$-periodic coefficients $q$ and $\omega$. It is shown that if 0 is a critical point of the operator $L$, then it is a singular critical point. This gives us a new class of $J$-positive differential operators with the singular critical point 0. Also, we extend the Beals and Parfenov regularity conditions for the critical point $\infty$ to the case of operators with periodic coefficients.
DOI
https://doi.org/10.7153/oam-05-50
Recommended Citation
Kostenko, A. (2010). The Similarity Problem for Indefinite Sturm-Liouville Operators With Periodic Coefficients. Operators and Matrices, vol. 5, no. 4, pg. 707-722. doi:10.7153/oam-05-50