Applications

The definition of \(\mathcal {Q}_{L}^{\left( n\right) }\) was given in ( 4.62 ) in terms of m-functions in \(\widetilde{\mathcal {M}} _{L}^{\left( n\right) }\) and \(\widetilde{\mathcal {M}}_{L}^{\left( n\right) }\) contains \(\mathcal {M}_{L}^{\left( n\right) }\) . \(\mathcal {M}_{L}^{\left( n\right) }\) is close to \(\widetilde{\mathcal {M}}_{L}^{\left( n\right) }\) , hence it is meaningful to find conditions of potentials q so that their WTK functions \(m_{\pm }\) satisfy (M.1), (M.2) (see ( 4.57 ), ( 4.58 )). In this section we provide concrete examples of this class including the well-known decaying and periodic cases.