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Inverse problem for interior spectral data of the Dirac operator on a finite interval. (English) Zbl 1021.34073

The authors consider the Dirac operator, generated by the differential expression

l(y)=By ' +Qy,0x1,

with

B=01-10,Q(x)=p(x)q(x)q(x)-p(x),y(x)=y 1 (x)y 2 (x),

subject to the boundary conditions

y 1 (0)cosα+y 2 (0)sinα=0,α[0,π),y 1 (1)cosβ+y 2 (1)sinβ=0,β[0,π)·

The authors prove uniqueness theorems taking the spectrum and the set of values of the eigenfunctions at some interior point as the given data.


MSC:
34L40Particular ordinary differential operators
34B24Sturm-Liouville theory
34L05General spectral theory for OD operators