Abstract:
We obtain the spectrum structures and the spectral decomposition of a non-self-adjoint differential operator $L$ generated by the differential expression $l[y]\equiv-y''+\alpha x^me^{i\mu x}y$, $m,\mu\ge1$, in the space $L_2(-\infty,\infty)$.
Keywords:non-self-adjoint differential operator, spectral decomposition of an operator, the space $L_2(-\infty,\infty)$, resolvent of an operator, rational function, holomorphic continuation.
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