The Lebesgue constants for the Franklin orthogonal system

• Autorzy: Z. Ciesielski , A. Kamont
• Języki publikacji: EN

Abstrakty

EN

To each set of knots $t_{i} = i/2n$ for i = 0,...,2ν and $t_{i} = (i-ν)/n$ for i = 2ν + 1,..., n + ν, with 1 ≤ ν ≤ n, there corresponds the space $𝓢_{ν,n}$ 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 $𝓢_{ν,n}$. The main result is
$lim_{(n-ν)∧ ν → ∞} ||P_{ν,n}||₁ = sup_{ν,n : 1 ≤ ν ≤ n} ||P_{ν,n}||₁ = 2 + (2 - √3)²$.
This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².

Kategorie tematyczne

• 41A15: Spline approximation
• 41A44: Best constants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 164
• Numer: 1
• Strony: 55-73

Daty

wydano

2004

Twórcy

autor

Z. Ciesielski

• Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland

autor

A. Kamont

• Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-825 Sopot, Poland

Identyfikatory

DOI

10.4064/sm164-1-4