The Lebesgue constants for the Franklin orthogonal system

Z. Ciesielski; A. Kamont

Z. Ciesielski ; A. Kamont

Studia Mathematica, Tome 162 (2004), p. 55-73 / Harvested from The Polish Digital Mathematics Library

Résumé

To each set of knots $t_{i} = i / 2 n$ for i = 0,...,2ν and $t_{i} = (i - ν) / n$ for i = 2ν + 1,..., n + ν, with 1 ≤ ν ≤ n, there corresponds the space $_{ν, n}$ of all piecewise linear and continuous functions on I = [0,1] with knots $t_{i}$ and the orthogonal projection $P_{ν, n}$ of L²(I) onto $_{ν, n}$ . The main result is $l i m_{(n - ν) \land ν \to \infty} | | P_{ν, n} | | ₁ = s u p_{ν, n : 1 \leq ν \leq n} | | P_{ν, n} | | ₁ = 2 + (2 - \sqrt 3) ²$ . This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².

Publié le : 2004-01-01

Zbl 1056.42021

EUDML-ID : urn:eudml:doc:284961

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     year = {2004},
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Z. Ciesielski; A. Kamont. The Lebesgue constants for the Franklin orthogonal system. Studia Mathematica, Tome 162 (2004) pp. 55-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-1-4/