TY - JOUR
T1 - Conjugate reciprocal polynomials with all roots on the unit circle
AU - Petersen, Kathleen L.
AU - Sinclair, Christopher D.
PY - 2008/10
Y1 - 2008/10
N2 - We study the geometry, topology and Lebesgue measure of the set of monk conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynomials of degree N is naturally associated to a subset of ℝN-1 . We calculate the volume of this set, prove the set is homeomorphic to the N - 1 ball and that its isometry group is isomorphic to the dihedral group of order 2N.
AB - We study the geometry, topology and Lebesgue measure of the set of monk conjugate reciprocal polynomials of fixed degree with all roots on the unit circle. The set of such polynomials of degree N is naturally associated to a subset of ℝN-1 . We calculate the volume of this set, prove the set is homeomorphic to the N - 1 ball and that its isometry group is isomorphic to the dihedral group of order 2N.
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U2 - 10.4153/CJM-2008-050-8
DO - 10.4153/CJM-2008-050-8
M3 - Article
AN - SCOPUS:53549127851
SN - 0008-414X
VL - 60
SP - 1149
EP - 1167
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 5
ER -