  Evolution operators of certain quantum walks possess, apart from the
continuous part, also point spectrum. The existence of eigenvalues and the
corresponding stationary states lead to partial trapping of the walker in the
vicinity of the origin. We analyze the stability of this feature for
three-state quantum walks on a line subject to homogenous coin deformations. We
find two classes of coin operators that preserve the point spectrum. These new
classes of coins are generalizations of coins found previously by different
methods and shed light on the rich spectrum of coins that can drive
discrete-time quantum walks.
