A convexity lemma on the interlacing inequalities for invariant factors
A simple proof is given for a lemma on divisibility of polynomials that was stated in an earlier paper of the author [ibid. 24, 33-50 (1979; Zbl 0395.15009)]. Two generalizations of the lemma are also stated. Reviewer's note: The presentation of the results is not complete, as the function \(\Delta\) (s) of Section 2 is - notwithstanding the author's assertion - not convex. The following data may serve as a simple counterexample: \(a_ i=b_ i=0\) for \(i\leq 0\), \(a_ 1=a_ 2=a_ 3=1\), \(a_ 4=2\), \(a_ i=i-1\) for \(i\geq 5\), \(b_ i=i\) for \(i\geq 1\); \(n=5.\) [Editorial remark: According to the reviewer's comment a correction has been submitted for this paper.]
scientific article; zbMATH DE number 4077449