Singular inner functions of \(L^1\)-type. II. (English) Zbl 0982.46037

Summary: In the first paper of the same title [J. Korean Math. Soc. 36, No. 4, 787-811 (1999; Zbl 0939.46032)], we introduced the concept of singular inner functions of \(L^1\)-type and obtained results for singular inner functions which are reminiscent of the results for weak infinite powers of Blaschke products. In this paper, we investigate singular inner functions for discrete measures. We give equivalent conditions on a measure for which it is a Blaschke type. And we prove that two discrete measures are mutually singular if and only if the associated common zero sets of singular inner functions of \(\ell^\infty_+\)-type do not meet.


46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30D50 Blaschke products, etc. (MSC2000)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)


Zbl 0939.46032
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