A nonregular case of the Jury test

The Jury test problem of determining the root distribution of a real polynomial with respect to the unit circle, was solved by Jury (1964), and was later simplified by Raible (1974). Keel (1999) presented a new simple proof of the Jury test. But they assumed that the characteristic polynomial has no root on the unit circle. However, this is the regular case. In this paper, we discuss a nonregular case in which all entries of some row of the Raible´s table become zero. Finally, we draw some important conclusions