In this article we study the spectral function for a nonsymmetric differential operator on the half line. Two cases of the coefficient matrix are considered, and for each case we prove by Marchenko's method that, to the boundary value problem, there corresponds a spectral function related to which a Marchenko-Parseval equality and an expansion formula are established. Our results extend the classical spectral theory for self-adjoint Sturm-Liouville operators and Dirac operators.
Submitted May 2, 2017. Published May 11, 2017.
Math Subject Classifications: 34L10, 47E05.
Key Words: Nonsymmetric first order differential operator; spectral function; expansion theorem.
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| Wuqing Ning |
School of Mathematical Sciences
University of Science and Technology of China
Hefei 230026, China
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