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Sampling and interpolation in de Branges spaces with doubling phase

Marzo, Jordi; Nitzan, Shahaf and Olsen, Jan-Fredrik LU (2012) In Journal d'Analyse Mathematique 117(1). p.365-395
Abstract
The de Branges spaces of entire functions generalize the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterization in terms of densities for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition is that the spaces we consider are model spaces generated by a one-component inner... (More)
The de Branges spaces of entire functions generalize the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterization in terms of densities for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition is that the spaces we consider are model spaces generated by a one-component inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and Ortega-CerdA for Fock spaces satisfying a doubling condition analogous to ours. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal d'Analyse Mathematique
volume
117
issue
1
pages
365 - 395
publisher
Magnes Press
external identifiers
  • wos:000305888100015
  • scopus:84863313037
ISSN
1565-8538
DOI
10.1007/s11854-012-0026-2
language
English
LU publication?
yes
id
a3c63fdf-082f-443d-830a-f2a261e4d449 (old id 3001778)
date added to LUP
2012-08-21 10:07:58
date last changed
2017-09-10 03:06:12
@article{a3c63fdf-082f-443d-830a-f2a261e4d449,
  abstract     = {The de Branges spaces of entire functions generalize the classical Paley-Wiener space of square summable bandlimited functions. Specifically, the square norm is computed on the real line with respect to weights given by the values of certain entire functions. For the Paley-Wiener space, this can be chosen to be an exponential function where the phase increases linearly. As our main result, we establish a natural geometric characterization in terms of densities for real sampling and interpolating sequences in the case when the derivative of the phase function merely gives a doubling measure on the real line. Moreover, a consequence of this doubling condition is that the spaces we consider are model spaces generated by a one-component inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and Ortega-CerdA for Fock spaces satisfying a doubling condition analogous to ours.},
  author       = {Marzo, Jordi and Nitzan, Shahaf and Olsen, Jan-Fredrik},
  issn         = {1565-8538},
  language     = {eng},
  number       = {1},
  pages        = {365--395},
  publisher    = {Magnes Press},
  series       = {Journal d'Analyse Mathematique},
  title        = {Sampling and interpolation in de Branges spaces with doubling phase},
  url          = {http://dx.doi.org/10.1007/s11854-012-0026-2},
  volume       = {117},
  year         = {2012},
}