Journal of Fourier Analysis and Applications

, Volume 23, Issue 6, pp 1426–1444 | Cite as

Adaptative Decomposition: The Case of the Drury–Arveson Space

  • Daniel Alpay
  • Fabrizio Colombo
  • Tao Qian
  • Irene Sabadini


The maximum selection principle allows to give expansions, in an adaptive way, of functions in the Hardy space \(\mathbf H_2\) 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 \(\mathbb C^N\), 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 \(\mathbb C^N\). 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.


Drury–Arveson space Adaptative decomposition Blaschke products 

Mathematics Subject Classification

47A56 41A20 



The authors thank the Macao Government FDCT 098/2012/A3 and D. Alpay thanks the Earl Katz family for endowing the chair which supported his research.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Daniel Alpay
    • 1
    • 2
  • Fabrizio Colombo
    • 3
  • Tao Qian
    • 4
  • Irene Sabadini
    • 3
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of mathematicsChapman UniversityOrangeUSA
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  4. 4.Department of MathematicsUniversity of MacauMacaoChina

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