Common zero sets of equivalent singular inner functions II
Let and be bounded positive singular measures on the unit circle such that ? . It is proved that there exist positive measures 0 and 0 such that 0 , 0 , and fj 0j < 1g\fj 0j < 1g =;, where is the associated singular inner function of . LetZ( ) = T f ; gZ( ) be the common zeros of equivalent singular inner functions of . Then Z( ) 6 ; and Z( )\Z( ) = ;. It follows that if and only ifZ( ) Z( ). HenceZ( ) is the set in the maximal ideal space of H 1 which