Finite interpolation on sequences in the disc

Laia Tugores

Archivum Mathematicum (2025)

  • Issue: 2, page 85-91
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Tugores, Laia. "Finite interpolation on sequences in the disc." Archivum Mathematicum (2025): 85-91. <http://eudml.org/doc/299991>.

@article{Tugores2025,
abstract = {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.},
author = {Tugores, Laia},
journal = {Archivum Mathematicum},
keywords = {interpolation on sequences; bounded analytic function; Lipschitz class; disc algebra},
language = {eng},
number = {2},
pages = {85-91},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Finite interpolation on sequences in the disc},
url = {http://eudml.org/doc/299991},
year = {2025},
}

TY - JOUR
AU - Tugores, Laia
TI - Finite interpolation on sequences in the disc
JO - Archivum Mathematicum
PY - 2025
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 2
SP - 85
EP - 91
AB - 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.
LA - eng
KW - interpolation on sequences; bounded analytic function; Lipschitz class; disc algebra
UR - http://eudml.org/doc/299991
ER -

References

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  1. Bruna, J., 10.1090/S0002-9947-1981-0603770-5, Trans. Amer. Math. Soc. 264 (2) (1981), 393–409. (1981) MR0603770DOI10.1090/S0002-9947-1981-0603770-5
  2. Burden, R.L., Faires, J.D., Numerical Analysis, Boston: PWS, 2010. (2010) 
  3. Dyn’kin, E.M., 10.1070/SM1980v037n01ABEH001944, Math. USSR Sbornik 37 (1) (1980), 97–117. (1980) DOI10.1070/SM1980v037n01ABEH001944
  4. Garnett, J.B., Bounded analytic functions, Grad. Texts Math., vol. 236, Springer Verlag, New York, 2006, Revised 1st. (2006) MR2261424
  5. Tugores, F., L., Tugores., 10.1556/314.2022.00013, Math. Pannon. (N.S.) 28 (2) (2022), 102–108. (2022) MR4495942DOI10.1556/314.2022.00013
  6. Vasyunin, V.I., 10.1007/BF02107247, J. Sov. Math. 31 (1985), 2660–2662. (1985) MR0741692DOI10.1007/BF02107247

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