Sampling and interpolation in de Branges spaces with doubling phase
(2012) In Journal d'Analyse Mathematique 117(1). p.365395 Abstract
 The de Branges spaces of entire functions generalize the classical PaleyWiener 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 PaleyWiener 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 onecomponent inner... (More)
 The de Branges spaces of entire functions generalize the classical PaleyWiener 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 PaleyWiener 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 onecomponent inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and OrtegaCerdA for Fock spaces satisfying a doubling condition analogous to ours. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3001778
 author
 Marzo, Jordi; Nitzan, Shahaf and Olsen, JanFredrik ^{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
 15658538
 DOI
 10.1007/s1185401200262
 language
 English
 LU publication?
 yes
 id
 a3c63fdf082f443d830af2a261e4d449 (old id 3001778)
 date added to LUP
 20120821 10:07:58
 date last changed
 20170910 03:06:12
@article{a3c63fdf082f443d830af2a261e4d449, abstract = {The de Branges spaces of entire functions generalize the classical PaleyWiener 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 PaleyWiener 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 onecomponent inner function. A novelty of our work is the application to de Branges spaces of techniques developed by Marco, Massaneda and OrtegaCerdA for Fock spaces satisfying a doubling condition analogous to ours.}, author = {Marzo, Jordi and Nitzan, Shahaf and Olsen, JanFredrik}, issn = {15658538}, language = {eng}, number = {1}, pages = {365395}, 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/s1185401200262}, volume = {117}, year = {2012}, }