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Cyclicity in Reproducing Kernel Hilbert Spaces of Analytic Functions

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Abstract

We introduce a large family of reproducing kernel Hilbert spaces \({\mathcal {H}} \subset \hbox {Hol}({\mathbb {D}})\), which include the classical Dirichlet-type spaces \(\mathcal {D}_\alpha \), by requiring normalized monomials to form a Riesz basis for \({\mathcal {H}}\). Then, after precisely evaluating the \(n\)th optimal norm and the \(n\)-th approximant of \(f(z)=1-z\), we completely characterize the cyclicity of functions in \(\hbox {Hol}(\overline{\mathbb {D}})\) with respect to the forward shift.

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Acknowledgments

The authors would like to thank Alan Sola for comments and suggestions.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, UFR de Mathématiques, Bâtiment M2, Université des Sciences et Technologies Lille 1, 59 655 , Villeneuve d’Ascq Cedex, France

    Emmanuel Fricain

  2. Départament de Mathematiques et de Statistique, Université Laval, Quebec, QC, G1K 7P4, Canada

    Javad Mashreghi

  3. Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, UK

    Daniel Seco

Authors
  1. Emmanuel Fricain
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  2. Javad Mashreghi
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  3. Daniel Seco
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Corresponding author

Correspondence to Daniel Seco.

Additional information

For this work, we were supported by grants from Labex CEMPI (ANR-11-LABX-0007-01), NSERC (100756), ERC Grant 2011-ADG-20110209 from EU programme FP2007-2013, MEC/MICINN Project MTM2011-24606, and Generalitat de Catalunya 2009SGR420.

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Fricain, E., Mashreghi, J. & Seco, D. Cyclicity in Reproducing Kernel Hilbert Spaces of Analytic Functions. Comput. Methods Funct. Theory 14, 665–680 (2014). https://doi.org/10.1007/s40315-014-0073-z

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  • DOI: https://doi.org/10.1007/s40315-014-0073-z

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