Eigenvalue estimates for singular left-definite Sturm-Liouville operators

Details Eigenvalue estimates for singular left-definite Sturm-Liouville operators Eigenvalue estimates for singular left-definite Sturm-Liouville operators

2010-12-19

arxiv.org/abs/1012.4195v2

Mathematics

Spectral Theory

to appear in J. Spectral Theory

Scientific paper

The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\subset\mathbb R^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is shown that the number of eigenvalues of $JA$ in $(-b,-a) \cup (a,b)$ differs at most by three of the number of eigenvalues of $A$ in the gap $(a,b)$; as a byproduct results on the accumulation of eigenvalues of singular left-definite Sturm-Liouville operators are obtained. Furthermore, left-definite problems with symmetric and periodic coefficients are treated, and several examples are included to illustrate the general results.

Affiliated with

Also associated with

No associations

Rating

Eigenvalue estimates for singular left-definite Sturm-Liouville operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Eigenvalue estimates for singular left-definite Sturm-Liouville operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenvalue estimates for singular left-definite Sturm-Liouville operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725728