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• W1915060452 abstract "Sufficient conditions for summability with speed of orthogonal series are found. 1. Main result Let φ = {φk} be a system of orthogonal functions on [a, b], and let λ = (λk) be a sequence with 0 < λk ↗∞. We will consider the series of the form ∑ ξkφk(t), where x = (ξk) ∈ `λ, i.e. ∑ ξ2 kλ 2 k <∞. We will use the following definitions from [1]. Let A = (ank) be a triangular summability method and let z = (ζk) ∈ c with lim ζk = ζ. The sequence z is said to be convergent with speed λ or λ-convergent, if the limit lim n λn(ζn − ζ) exists. The set of all λ-convergent sequences is denoted by cλ. The sequence z is said to be A-summable with speed λ or Aλ-summable, if y = (ηn) ∈ cλ, where ηn = n ∑ k=0 ankζk. The summability method A is said to be λ-convergence preserving if every element of the set cλ is Aλ-summable. 2000 Mathematics Subject Classification. 40C05, 42C15." @default.
• W1915060452 created "2016-06-24" @default.
• W1915060452 creator A5026859003 @default.
• W1915060452 date "2005-01-01" @default.
• W1915060452 modified "2023-09-27" @default.
• W1915060452 title "Convergence and summability with speed of functional series" @default.
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