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Refined asymptotic formulas for eigenvalues and eigenfunctions of the Dirac system. (English. Russian original) Zbl 1258.34171

Dokl. Math. 85, No. 2, 240-242 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 443, No. 4, 414-417 (2012).
The authors study the Dirac system \[ \begin{aligned} &y'_1 (x) - q_2 (x)y_2 (x) = \lambda y_1 (x), \\ &y'_2 (x) - q_1 (x)y_1 (x) = - \lambda y_2 (x)\end{aligned} \] with boundary conditions \[ y_1 (0) = y_2 (0),\,\,\,\,\,y_1 (1) = y_2 (1). \] Using a method based on transformation operator formulas, refined asymptotic formulas for the nonsmooth case are given.

MSC:

34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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References:

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