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Local properties of Hilbert spaces of Dirichlet series

Olsen, Jan-Fredrik LU (2011) In Journal of Functional Analysis 261(9). p.2669-2696
Abstract
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite-dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite-dimensional unit ball. We use both techniques... (More)
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite-dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite-dimensional unit ball. We use both techniques from the theory of sampling in Paley-Wiener spaces, and classical results from analytic number theory. (C) 2011 Elsevier Inc. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Dirichlet series, Hardy space in infinitely many complex variables, Carleson measures
in
Journal of Functional Analysis
volume
261
issue
9
pages
2669 - 2696
publisher
Elsevier
external identifiers
  • wos:000294703500014
  • scopus:80052096499
ISSN
0022-1236
DOI
10.1016/j.jfa.2011.07.007
language
English
LU publication?
yes
id
57f44c5a-bd0e-4240-a3ec-c3022268629b (old id 2186857)
date added to LUP
2011-10-24 12:40:25
date last changed
2017-01-01 05:50:32
@article{57f44c5a-bd0e-4240-a3ec-c3022268629b,
  abstract     = {We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite-dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite-dimensional unit ball. We use both techniques from the theory of sampling in Paley-Wiener spaces, and classical results from analytic number theory. (C) 2011 Elsevier Inc. All rights reserved.},
  author       = {Olsen, Jan-Fredrik},
  issn         = {0022-1236},
  keyword      = {Dirichlet series,Hardy space in infinitely many complex variables,Carleson measures},
  language     = {eng},
  number       = {9},
  pages        = {2669--2696},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Local properties of Hilbert spaces of Dirichlet series},
  url          = {http://dx.doi.org/10.1016/j.jfa.2011.07.007},
  volume       = {261},
  year         = {2011},
}