Functional models and asymptotically orthonormal sequences

Isabelle Chalendar[1]; Emmanuel Fricain[1]; Dan Timotin[2]

  • [1] Université Claude Bernard Lyon I, Institut Girard Desargues, UFR de Mathématiques, 69622 Villeurbanne Cedex (France)
  • [2] Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 70700 (Romania)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 5, page 1527-1549
  • ISSN: 0373-0956

Abstract

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Suppose H 2 is the Hardy space of the unit disc in the complex plane, while Θ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space K Θ = H 2 ⊖ Θ H 2 to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

How to cite

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Chalendar, Isabelle, Fricain, Emmanuel, and Timotin, Dan. "Functional models and asymptotically orthonormal sequences." Annales de l’institut Fourier 53.5 (2003): 1527-1549. <http://eudml.org/doc/116080>.

@article{Chalendar2003,
abstract = {Suppose $H^2$ is the Hardy space of the unit disc in the complex plane, while $\Theta $ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space $K_\Theta =H^2\ominus \Theta H^2$ to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.},
affiliation = {Université Claude Bernard Lyon I, Institut Girard Desargues, UFR de Mathématiques, 69622 Villeurbanne Cedex (France); Université Claude Bernard Lyon I, Institut Girard Desargues, UFR de Mathématiques, 69622 Villeurbanne Cedex (France); Institute of Mathematics of the Romanian Academy, PO Box 1-764, Bucharest 70700 (Romania)},
author = {Chalendar, Isabelle, Fricain, Emmanuel, Timotin, Dan},
journal = {Annales de l’institut Fourier},
keywords = {Hardy space; functional model; asymptotically orthornormal sequence; asymptotically orthonormal sequence},
language = {eng},
number = {5},
pages = {1527-1549},
publisher = {Association des Annales de l'Institut Fourier},
title = {Functional models and asymptotically orthonormal sequences},
url = {http://eudml.org/doc/116080},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Chalendar, Isabelle
AU - Fricain, Emmanuel
AU - Timotin, Dan
TI - Functional models and asymptotically orthonormal sequences
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 5
SP - 1527
EP - 1549
AB - Suppose $H^2$ is the Hardy space of the unit disc in the complex plane, while $\Theta $ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space $K_\Theta =H^2\ominus \Theta H^2$ to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.
LA - eng
KW - Hardy space; functional model; asymptotically orthornormal sequence; asymptotically orthonormal sequence
UR - http://eudml.org/doc/116080
ER -

References

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  14. B. Sz-Nagy, C. Foias, Harmonic Analysis of Operators on Hilbert Spaces, (1970), North-Holland Publishing Co., Amsterdam-London Zbl0201.45003MR275190
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