The Lebesgue constants for the Franklin orthogonal system

Z. Ciesielski, and A. Kamont. "The Lebesgue constants for the Franklin orthogonal system." Studia Mathematica 164.1 (2004): 55-73. <http://eudml.org/doc/284961>.

@article{Z2004,
abstract = {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 $_\{ν,n\}$ 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 $lim_\{(n-ν)∧ ν → ∞\} ||P_\{ν,n\}||₁ = sup_\{ν,n : 1 ≤ ν ≤ n\} ||P_\{ν,n\}||₁ = 2 + (2 - √3)²$. This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².},
author = {Z. Ciesielski, A. Kamont},
journal = {Studia Mathematica},
keywords = {Lebesgue constant; Franklin system; Franklin-Strömberg wavelet},
language = {eng},
number = {1},
pages = {55-73},
title = {The Lebesgue constants for the Franklin orthogonal system},
url = {http://eudml.org/doc/284961},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Z. Ciesielski
AU - A. Kamont
TI - The Lebesgue constants for the Franklin orthogonal system
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 1
SP - 55
EP - 73
AB - 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 $_{ν,n}$ 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 $lim_{(n-ν)∧ ν → ∞} ||P_{ν,n}||₁ = sup_{ν,n : 1 ≤ ν ≤ n} ||P_{ν,n}||₁ = 2 + (2 - √3)²$. This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².
LA - eng
KW - Lebesgue constant; Franklin system; Franklin-Strömberg wavelet
UR - http://eudml.org/doc/284961
ER -