Sampling and interpolation in de Branges spaces with doubling phase
(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:
https://lup.lub.lu.se/record/3001778
- author
- Marzo, Jordi ; Nitzan, Shahaf and Olsen, Jan-Fredrik LU
- organization
- publishing date
- 2012
- 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
- 2016-04-01 10:04:57
- date last changed
- 2022-03-27 04:39:48
@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}},
doi = {{10.1007/s11854-012-0026-2}},
volume = {{117}},
year = {{2012}},
}