Nontangential interpolating sequences and interpolation by normal functions

Author:
Kam-fook Tse

Journal:
Proc. Amer. Math. Soc. **29** (1971), 351-354

MSC:
Primary 30.70

MathSciNet review:
0274777

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Abstract: The first part of the paper shows that a sequence of points in the unit disk of the complex plane, tending nontangentially to a point on the unit circle, is an interpolating sequence if and only if the pseudo-hyperbolic distance between any pair of points in the sequence is bounded away from zero. The second part shows that interpolating sequences for bounded analytic functions are also interpolating sequences for normal functions.

**[1]**Lennart Carleson,*An interpolation problem for bounded analytic functions*, Amer. J. Math.**80**(1958), 921–930. MR**0117349****[2]**Joseph A. Cima and Peter Colwell,*Blaschke quotients and normality*, Proc. Amer. Math. Soc.**19**(1968), 796–798. MR**0227423**, 10.1090/S0002-9939-1968-0227423-X**[3]**Peter Lappan,*Some sequential properties of normal and non-normal functions with applications to automorphic functions*, Comment. Math. Univ. St. Paul.**12**(1964), 41–57. MR**0162946****[4]**D. J. Newman,*Interpolation in 𝐻^{∞}*, Trans. Amer. Math. Soc.**92**(1959), 501–507. MR**0117350**, 10.1090/S0002-9947-1959-0117350-X**[5]**Kam-fook Tse,*On the sums and products of normal functions*, Comment. Math. Univ. St. Paul.**17**(1969), 63–72. MR**0268385**

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DOI:
https://doi.org/10.1090/S0002-9939-1971-0274777-4

Keywords:
Pseudo-hyperbolic distance,
interpolating sequence,
Blaschke product,
Blaschke sequence,
normal function

Article copyright:
© Copyright 1971
American Mathematical Society