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Peer-reviewedCC BY 4.0Research in the Mathematical Sciences

Lower bounds in H2-rational approximation to Blaschke products

  • Laurent Baratchart
  • Alexander Borichev
  • Sylvain Chevillard
  • Claire Coiffard Marre
  • Rachid Zarouf
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Abstract

We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space H2 of the unit disk. We first consider approximation to zN, and then move on to more general Blaschke products whose zeros are bounded away from the circle. The latter case depends on Fourier coefficients estimates for Blaschke products which are of independent interest.

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Cite

BibTeXRIS
BibTeX
@article{baratchart2026lower,
  title = {{Lower bounds in $H^2$-rational approximation to Blaschke products}},
  author = {Laurent Baratchart and Alexander Borichev and Sylvain Chevillard and Claire Coiffard Marre and Rachid Zarouf},
  journal = {Research in the Mathematical Sciences},
  year = {2026},
  month = sep,
  doi = {10.1007/s40687-026-00657-4},
  eprint = {2603.16295},
  archivePrefix = {arXiv},
  url = {https://inria.hal.science/hal-05385529v3},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Lower bounds in H^2-rational approximation to Blaschke products
AU  - Laurent Baratchart
AU  - Alexander Borichev
AU  - Sylvain Chevillard
AU  - Claire Coiffard Marre
AU  - Rachid Zarouf
PY  - 2026
DA  - 2026/09/28
JO  - Research in the Mathematical Sciences
DO  - 10.1007/s40687-026-00657-4
UR  - https://inria.hal.science/hal-05385529v3
AB  - We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space H^2 of the unit disk. We first consider approximation to z^N, and then move on to more general Blaschke products whose zeros are bounded away from the circle. The latter case depends on Fourier coefficients estimates for Blaschke products which are of independent interest.
SN  - 2522-0144
SN  - 2197-9847
ER  -