Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 7 - Probabilistic Tools I

  • from Part 1 - Bohr’s Problem and Complex Analysis on Polydiscs
  • Andreas Defant, Carl V. Ossietzky Universität Oldenburg, Germany, Domingo García, Universitat de València, Spain, Manuel Maestre, Universitat de València, Spain, Pablo Sevilla-Peris
  • Book:
    Dirichlet Series and Holomorphic Functions in High Dimensions
    Published online:
    19 July 2019
    Print publication:
    08 August 2019, pp 153-180

  • Summary

    We give an alternative, probabilistic, approach to two of the subjects considered so far: the optimality of the exponent in the polynomial Bohnenblust-Hille inequality (see Chapter 6) and the lower bound for S in Bohr’s problem (see Chapters 1 and 4). We use a probabilistic device: the Kahane-Salem-Zygmund inequality. This shows that, for a given finite family of coefficients, a choice of signs can be found in such a way that the polynomial whose coefficients are the original ones multiplied by the signs has small norm (supremum on the polydisc). The proof uses Bernstein’s inequality and Rademacher random variables. We also look at the relationship between Rademacher and Steinhaus random variables, and deduce the classical Khinchin inequality from the Khinchin-Steinhaus inequality (see Chapter 6). We consider Dirichlet series, place signs before the coefficients, and define the almost sure abscissas (in each of the senses from Chapter 1) by considering each convergence for almost every choice of signs. An analogue of Bohr’s problem in this sense is considered.