Geodesic
The Lebesgue constants for the Franklin orthogonal system
Z. Ciesielski1 ; A. Kamont1
1 Institute of Mathematics Polish Academy of Sciences Abrahama 18 81-825 Sopot, Poland
Studia Mathematica, Tome 164 (2004) no. 1, pp. 55-73

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

To each set of knots $t_i = {i/ 2n}$ for $i=0,\dots ,2\nu$ and $t_i= {(i-\nu) / n}$ for $i=2\nu +1,\dots, n+\nu $, with $1\leq \nu\leq n$, there corresponds the space ${\cal S}_{\nu ,n}$ of all piecewise linear and continuous functions on $I=[0,1]$ with knots $t_i$ and the orthogonal projection $P_{\nu ,n}$ of $L^2(I)$ onto ${\cal S}_{\nu ,n}$. The main result is $$ \lim_{(n-\nu)\wedge\nu\to\infty}\|P_{\nu ,n}\|_1 = \sup_{\nu ,n\,:\,1\leq \nu\leq n}\|P_{\nu ,n}\|_1 = 2+(2-\sqrt{3})^2. $$ This shows that the Lebesgue constant for the Franklin orthogonal system is $2+(2-\sqrt{3})^2$.
DOI : 10.4064/sm164-1-4
Mots-clés : each set knots dots i dots leq leq there corresponds space cal piecewise linear continuous functions knots orthogonal projection cal main result lim n wedge infty sup leq leq sqrt shows lebesgue constant franklin orthogonal system sqrt

Z. Ciesielski 1 ; A. Kamont 1

1 Institute of Mathematics Polish Academy of Sciences Abrahama 18 81-825 Sopot, Poland 
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Z. Ciesielski; A. Kamont. The Lebesgue constants for the Franklin orthogonal system. Studia Mathematica, Tome 164 (2004) no. 1, pp. 55-73. doi: 10.4064/sm164-1-4

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