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On Asymptotically Orthonormal Sequences

  Published:2017-03-31
 Printed: Dec 2017
  • Emmanuel Fricain,
    Laboratoire Paul Painlevé, Université Lille 1, 59 655 Villeneuve d'Ascq Cédex
  • Rishika Rupam,
    Laboratoire Paul Painlevé, Université Lille 1, 59 655 Villeneuve d'Ascq Cédex
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Abstract

An asymptotically orthonormal sequence is a sequence which is "nearly" orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels for model spaces and de Branges-Rovnyak spaces.
Keywords: function space, de Branges-Rovnyak and model space, reproducing kernel, asymptotically orthonormal sequence function space, de Branges-Rovnyak and model space, reproducing kernel, asymptotically orthonormal sequence
MSC Classifications: 30J05, 30H10, 46E22 show english descriptions Inner functions
Hardy spaces
Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
30J05 - Inner functions
30H10 - Hardy spaces
46E22 - Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
 

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