[51–1] Special Conformal, Mappings

Fejér, Leopold; Szegő, G.

doi:10.1007/978-1-4612-5785-1_12

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2003

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“…Following Fejér and Szegő [5], consider the Cesàro sums S j m (ζ) of order j of the geometric series,…”

Section: Proof Of Theoremmentioning

confidence: 99%

An Extremal Nonnegative Sine Polynomial

Andreani¹,

Dimitrov²

2003

Rocky Mountain J. Math.

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For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials K n (θ) are constructed in such a way that {K n (θ)} is a summability kernel. Thus, for each p, 1 ≤ p ≤ ∞ and for any 2π-periodic function f ∈ L p [−π, π], the sequence of convolutions K n * f is proved to converge to f in L p [−π, π]. The pointwise and almost everywhere convergences are also consequences of our construction.

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“…Following Fejér and Szegő [5], consider the Cesàro sums S j m (ζ) of order j of the geometric series,…”

Section: Proof Of Theoremmentioning

confidence: 99%