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Keywords:
interpolation on sequences; bounded analytic function; Lipschitz class; disc algebra
interpolation on sequences; bounded analytic function; Lipschitz class; disc algebra
Summary:
This note deals with interpolation of values of analytic functions belonging to a given space, on finite sets of consecutive points of sequences in the disc, performed by rational functions and polynomials. Our goal is to identify sequences and spaces whose functions provide a bound of the error at the first uninterpolated point that is as small as desired. For certain sequences, we prove that this happens for bounded functions, Lipschitz functions and those that have derivatives in the disc algebra.
References:
[1] Bruna, J.: Boundary interpolation sets for holomorphic functions smooth up to the boundary and BMO. Trans. Amer. Math. Soc. 264 (2) (1981), 393–409. DOI 10.1090/S0002-9947-1981-0603770-5 | MR 0603770
[2] Burden, R.L., Faires, J.D.: Numerical Analysis. Boston: PWS, 2010.
[3] Dyn’kin, E.M.: Free interpolation sets for Hölder classes. Math. USSR Sbornik 37 (1) (1980), 97–117. DOI 10.1070/SM1980v037n01ABEH001944
[4] Garnett, J.B.: Bounded analytic functions. Grad. Texts Math., vol. 236, Springer Verlag, New York, 2006, Revised 1st. MR 2261424
[5] Tugores, F., L., Tugores.: Polynomial interpolation on sequences. Math. Pannon. (N.S.) 28 (2) (2022), 102–108. DOI 10.1556/314.2022.00013 | MR 4495942
[6] Vasyunin, V.I.: Characterization of finite unions of Carleson sets in terms of solvability of interpolational problems. J. Sov. Math. 31 (1985), 2660–2662. DOI 10.1007/BF02107247 | MR 0741692
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