Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Optimal interpolation in Hardy and Bergman spaces: A reproducing kernel Banach space approach
HTML articles powered by AMS MathViewer

by Gilbert J. Groenewald, Sanne ter Horst and Hugo J. Woerdeman;
Trans. Amer. Math. Soc. 378 (2025), 4303-4333
DOI: https://doi.org/10.1090/tran/9389
Published electronically: March 19, 2025

Abstract:

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1<p<\infty$, on the unit ball in $\mathbb {C}^n$, as well as the Hardy space on the polydisk and half-space. In particular, we show how the framework leads to a procedure to find a minimal norm element $f$ satisfying interpolation conditions $f(z_j)=w_j$, $j=1,\ldots , n$. We also explain the techniques in the setting of $\ell ^p$ spaces where the norm is defined via a change of variables and provide numerical examples.
References
Similar Articles
Bibliographic Information
  • Gilbert J. Groenewald
  • Affiliation: School of Mathematical and Statistical Sciences, North-West University, Private Bag X6001, Potchefstroom 2520, South Africa
  • MR Author ID: 349945
  • ORCID: 0000-0002-1658-3648
  • Email: Gilbert.Groenewald@nwu.ac.za
  • Sanne ter Horst
  • Affiliation: School of Mathematical and Statistical Sciences, North-West University, Private Bag X6001, Potchefstroom 2520, South Africa; and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa
  • MR Author ID: 776159
  • ORCID: 0000-0003-2562-3370
  • Email: Sanne.TerHorst@nwu.ac.za
  • Hugo J. Woerdeman
  • Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
  • MR Author ID: 183930
  • ORCID: 0000-0002-8538-7173
  • Email: hugo@math.drexel.edu
  • Received by editor(s): February 22, 2024
  • Received by editor(s) in revised form: December 3, 2024
  • Published electronically: March 19, 2025
  • Additional Notes: This work was based on the research supported in part by the National Research Foundation of South Africa (Grant Numbers 118513 and 127364) and the DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS). In addition, the third author was partially supported by NSF grant DMS-2000037.
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 4303-4333
  • MSC (2020): Primary 46E15, 42B30, 30H10, 46B10, 46B25
  • DOI: https://doi.org/10.1090/tran/9389