The n-width of the unit ball of Hq

S. D. Fisher; M. I. Stessin

doi:10.1016/0021-9045(91)90009-Y

The n-width of the unit ball of H^q

S. D. Fisher
, M. I. Stessin

Mathematics and Statistics

University at Albany

Northwestern University

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

19 Scopus citations

Abstract

Let E be a compact subset of the open unit disc Δ and let H^q be the Hardy space of analytic functions f on Δ for which stf|^q has a harmonic majorant. We determine the value of the Kolmogorov, Gel'fand, and linear n-widths in L^p(E, μ) of the restriction to E of the unit ball of H^q when p ≤ q or when 1 ≤ q < p < ∞ and E is "small".

Original language	English
Pages (from-to)	347-356
Number of pages	10
Journal	Journal of Approximation Theory
Volume	67
Issue number	3
DOIs	https://doi.org/10.1016/0021-9045(91)90009-Y
State	Published - Dec 1991

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10.1016/0021-9045(91)90009-Y

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title = "The n-width of the unit ball of Hq",

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AU - Stessin, M. I.

PY - 1991/12

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N2 - Let E be a compact subset of the open unit disc Δ and let Hq be the Hardy space of analytic functions f on Δ for which stf|q has a harmonic majorant. We determine the value of the Kolmogorov, Gel'fand, and linear n-widths in Lp(E, μ) of the restriction to E of the unit ball of Hq when p ≤ q or when 1 ≤ q < p < ∞ and E is "small".

AB - Let E be a compact subset of the open unit disc Δ and let Hq be the Hardy space of analytic functions f on Δ for which stf|q has a harmonic majorant. We determine the value of the Kolmogorov, Gel'fand, and linear n-widths in Lp(E, μ) of the restriction to E of the unit ball of Hq when p ≤ q or when 1 ≤ q < p < ∞ and E is "small".

UR - https://www.scopus.com/pages/publications/38149145297

U2 - 10.1016/0021-9045(91)90009-Y

DO - 10.1016/0021-9045(91)90009-Y

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VL - 67

SP - 347

EP - 356

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 3

ER -

The n-width of the unit ball of H^q

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