On the divergence of greedy algorithms with respect to Walsh subsystems in

Episkoposian, Sergo A.

doi:10.1016/j.na.2006.02.023

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Cited by 6 publications

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“…That is, statements (1)-( 3) of Lemma 2.4 are satisfied. Now we will check the fulfillment of statement (4).…”

Section: )mentioning

confidence: 99%

On the existence of universal series by the generalized Walsh system

Episkoposian¹

2016

Banach J. Math. Anal.

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In this paper, we prove the following: let ω(t) be a continuous function with ω(+0) = 0 and increasing in [0, ∞). Then there exists a series of the formwith the following property: for each ε > 0 a weight function µ(x), 0 < µ(x) ≤ 1, |{x ∈ [0, 1) : µ(x) = 1}| < ε can be constructed so that the series is universal in the weighted space L 1 µ [0, 1) both with respect to rearrangements and subseries.

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“…That is, statements (1)-( 3) of Lemma 2.4 are satisfied. Now we will check the fulfillment of statement (4).…”

Section: )mentioning

confidence: 99%