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Keywords:
interpolating sequences; bounded analytic functions; separated sequences
interpolating sequences; bounded analytic functions; separated sequences
Summary:
This note deals with the classical topic of interpolating bounded sequences of complex numbers by bounded analytic functions on sequences in the unit disk. We introduce linear, polynomial, and multiplicative interpolation over fixed-length consecutive blocks of points taken from these sequences, and examine the corresponding interpolating sequences.
References:
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[2] Garnett, J.B.: Bounded analytic functions. Grad. Texts in Math., vol. 236, Springer Verlag, New York, 2006, revised 1st. MR 2261424
[3] Tugores, F.: Recursive interpolating sequences. Open Math. 16 (2018), 461–468. DOI 10.1515/math-2018-0044 | MR 3797927
[4] Tugores, F., Tugores, L.: Interpolation by differences in $H^\infty $. Stud. Sci. Math. Hungar. 58 (2021), 157–162. MR 4296469
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