Isospectral Mathieu-Hill Operators

Details Isospectral Mathieu-Hill Operators Isospectral Mathieu-Hill Operators

2012-02-27

arxiv.org/abs/1202.6048v3

Mathematics

Spectral Theory

Scientific paper

In this paper we prove that the spectrum of the Mathieu-Hill Operators with potentials ae^{-i2{\pi}x}+be^{i2{\pi}x} and ce^{-i2{\pi}x}+de^{i2{\pi}x} are the same if and only if ab=cd, where a,b,c and d are complex numbers. This result implies some corollaries about the extension of Harrell-Avron-Simon formula. Moreover, we find explicit formulas for the eigenvalues and eigenfunctions of the t-periodic boundary value problem for the Hill operator with Gasymov's potential.

Affiliated with

Also associated with

No associations

Rating

Isospectral Mathieu-Hill 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 Isospectral Mathieu-Hill Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isospectral Mathieu-Hill Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-605047