Local properties of Hilbert spaces of Dirichlet series

Mathematics – Complex Variables

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

27 pages, 1 figure

Scientific paper

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Local properties of Hilbert spaces of Dirichlet series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Local properties of Hilbert spaces of Dirichlet series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Local properties of Hilbert spaces of Dirichlet series will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-298725

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.