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This paper is a continuation of the paper \cite{W} by the third author, whichstudied quantum walks with special long-range perturbations of the coinoperator. In this paper, we consider general long-range perturbations of thecoin operator and prove the non-existence of a singular continuous spectrum andembedded eigenvalues. The proof relies on the construction of generalizedeigenfunctions (Jost solutions) which was studied in the short-range case in\cite{MSSSSdis}.

Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins