## Some $H^{\infty }$-interpolating sequences and the behavior of certain of their Blaschke products

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- by Max L. Weiss PDF
- Trans. Amer. Math. Soc.
**209**(1975), 211-223 Request permission

## Abstract:

Let $f$ be a strictly increasing continuous real function defined near ${0^ + }$ with $f(0) = fâ(0) = 0$. Such a function is called a $K$-function if for every constant $k,f(\theta + kf(\theta ))/f(\theta ) \to 1/$ as $\theta \to {0^ + }$. The curve in the open unit disc with corresponding representation $1 - r = f(\theta )$ is called a $K$-curve. Several analytic and geometric conditions are obtained for $K$-curves and $K$-functions. This provides a framework for some rather explicit results involving parts in the closure of $K$-curves, ${H^\infty }$-interpolating sequences lying on $K$-curves and the behavior of their Blaschke products. In addition, a sequence of points in the disc tending upper tangentially to 1 with moduli increasing strictly to 1 and arguments decreasing strictly to 0 is proved to be interpolating if and only if the hyperbolic distance between successive points remains bounded away from zero.## References

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## Additional Information

- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**209**(1975), 211-223 - MSC: Primary 30A98; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1975-0372219-X
- MathSciNet review: 0372219