Adaptative Decomposition: The Case of the Drury–Arveson Space

Daniel Alpay; Fabrizio Colombo; Tao Qian; Irene Sabadini

doi:10.1007/s00041-016-9508-4

Adaptative Decomposition: The Case of the Drury–Arveson Space

Daniel Alpay, Fabrizio Colombo, Tao Qian, Irene Sabadini

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 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 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 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.

Original language	English
Pages (from-to)	1426-1444
Number of pages	19
Journal	Journal of Fourier Analysis and Applications
Volume	23
Issue number	6
DOIs	https://doi.org/10.1007/s00041-016-9508-4
State	Published - 1 Dec 2017

Keywords

Adaptative decomposition
Blaschke products
Drury–Arveson space

ASJC Scopus subject areas

Analysis
General Mathematics
Applied Mathematics

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10.1007/s00041-016-9508-4

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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.",

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AU - Qian, Tao

AU - Sabadini, Irene

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AB - 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.

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Adaptative Decomposition: The Case of the Drury–Arveson Space

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Keywords

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