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No Entire Inner Functions

Abstract

We study generalized inner functions on a large family of Reproducing Kernel Hilbert Spaces. We show that the only inner functions which are entire are the normalized monomials.

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Acknowledgements

The authors thank I. Efraimidis, M. Hartz and the anonymous referee for careful reading and valuable comments.

Author information

Correspondence to D. Seco.

Additional information

The authors acknowledge the financial support by the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2015-0554) at ICMAT.

The second author is also grateful for support from the Spanish Ministry of Economy and Competitiveness, through grant MTM2016-77710-P.

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Cite this article

Cobos, A., Seco, D. No Entire Inner Functions. Anal Math 46, 39–45 (2020). https://doi.org/10.1007/s10476-020-0015-0

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Key words and phrases

  • Reproducing kernel Hilbert space
  • inner function
  • Dirichlet space

Mathematics Subject Classification

  • primary 30J05
  • secondary 30H05
  • 30H10
  • 47A15