Floquet theory revisited. (English) Zbl 0946.47031
Knowles, Ian (ed.), Differential equations and mathematical physics. Proceedings of the conference, University of Alabama, Birmingham, AL, USA and Georgia Institute of Technology, Atlanta, GA, USA, March 13-17, 1994. Cambridge, MA: International Press. 67-84 (1995).
The authors consider the scalar second order differential operator
\[
L=\frac{d^2}{dx^2}+q(x)
\]
with a complex-valued periodic finite gap potential of period \(\Omega>0\) and construct the two-sheeted hyperelliptic surface associated with this operator. Moreover, the difference between the self-adjoint and non-self-adjoint cases is illustrated by studying algebraic and geometric multiplicities of eigenvalues of \(L\) over a periodicity interval \([x_0,x_0+L]\) and computing the corresponding Fredholm determinants.
For the entire collection see [Zbl 0915.00042].
For the entire collection see [Zbl 0915.00042].
Reviewer: Serguei Zelik (Moskva)
MSC:
| 47E05 | General theory of ordinary differential operators |
| 34B05 | Linear boundary value problems for ordinary differential equations |
