## Journal of the Mathematical Society of Japan

### Singular inner functions of $L^{1}$-type II

Keiji IZUCHI

#### Abstract

In the first paper of the same title, 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 $t_{+}^{\infty}$-type do not meet.

#### Article information

Source
J. Math. Soc. Japan, Volume 53, Number 2 (2001), 285-305.

Dates
First available in Project Euclid: 9 June 2008

https://projecteuclid.org/euclid.jmsj/1213023458

Digital Object Identifier
doi:10.2969/jmsj/05320285

Mathematical Reviews number (MathSciNet)
MR1815135

Zentralblatt MATH identifier
0982.46037

#### Citation

IZUCHI, Keiji. Singular inner functions of $L^{1}$ -type II. J. Math. Soc. Japan 53 (2001), no. 2, 285--305. doi:10.2969/jmsj/05320285. https://projecteuclid.org/euclid.jmsj/1213023458