Adaptative Decomposition: The Case of the Drury–Arveson Space

Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The maximum selection principle allows to give expansions, in an adaptive way, of functions in the Hardy space H2 of the disk in terms of Blaschke products. The expansion is specific to the given function. Blaschke factors and products have counterparts in the unit ball of CN, and this fact allows us to extend in the present paper the maximum selection principle to the case of functions in the Drury–Arveson space of functions analytic in the unit ball of CN. This will give rise to an algorithm which is a variation in this higher dimensional case of the greedy algorithm. We also introduce infinite Blaschke products in this setting and study their convergence.

Original languageEnglish
Pages (from-to)1426-1444
Number of pages19
JournalJournal of Fourier Analysis and Applications
Volume23
Issue number6
DOIs
StatePublished - 1 Dec 2017

Keywords

  • Adaptative decomposition
  • Blaschke products
  • Drury–Arveson space

ASJC Scopus subject areas

  • Analysis
  • Mathematics (all)
  • Applied Mathematics

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