Construct a Massive Dirac Operator with a Number of Eigenvalues in a Continuous Spectrum
DOI:
https://doi.org/10.31150/ajshr.v2i6.525Keywords:
Dirac operator, operator spectrum, discrete spectrum, continuous spectrum, Weil – Titchmarch function, Gelfand-Levitan integral equation, matrix function, Heveside functionAbstract
A massive Dirac operator with a number of eigenvalues is constructed in the continuous spectrum, and sufficient conditions are found for this operator to belong to the space of coefficients. The dependence of the eigenvalues of the mass Dirac operator on the continuous spectrum on the general boundary conditions is studied. for the following Dirac operator, which is self-contained in the space of vector functions
in the case of
, .
the Weil – Titchmarch function, which satisfies the initial conditions, is defined as a single value.
The coefficients of the operator are as follows
Found using the Gelfand-Levitan integral equation.
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