Common zero sets of equivalent singular inner functions

Keiji Izuchi
2004 Studia Mathematica  
Let µ and λ be bounded positive singular measures on the unit circle such that µ ⊥ λ. It is proved that there exist positive measures µ 0 and λ 0 such that µ 0 ∼ µ, be the common zeros of equivalent singular inner functions of ψ µ . Then Z(µ) = ∅ and Z(µ) ∩ Z(λ) = ∅. It follows that µ λ if and only if Z(µ) ⊂ Z(λ). Hence Z(µ) is the set in the maximal ideal space of H ∞ which relates naturally to the set of measures equivalent to µ. Some basic properties of Z(µ) are given. 2000 Mathematics
more » ... 0 Mathematics Subject Classification: Primary 46J15.
doi:10.4064/sm163-3-3 fatcat:z3eriemlubd67jcyczumir5z6q