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Deforming the point spectra of one-dimensional Dirac operators. (English) Zbl 0899.34052

Summary: The author provides a method of inserting and removing any finite number of prescribed eigenvalues into spectral gaps of a given one-dimensional Dirac operator. This is done in such a way that the original and deformed operators are unitarily equivalent when restricted to the complement of the subspace spanned by the newly inserted eigenvalue. Moreover, the unitary transformation operator which links the original operator to its deformed version is explicitly determined.

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47B25 Linear symmetric and selfadjoint operators (unbounded)
34B05 Linear boundary value problems for ordinary differential equations
34L05 General spectral theory of ordinary differential operators
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