Uniform convergence of the greedy algorithm with respect to the Walsh system

• Autorzy: Martin Grigoryan
• Języki publikacji: EN

Abstrakty

EN

For any 0 < ϵ < 1, p ≥ 1 and each function $f ∈ L^{p}[0,1]$ one can find a function $g ∈ L^{∞}[0,1)$ with mes{x ∈ [0,1): g ≠ f} < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence ${|c_{k}(g)|: k ∈ spec(g)}$ is decreasing, where ${c_{k}(g)}$ is the sequence of Fourier coefficients of g with respect to the Walsh system.

Kategorie tematyczne

• 42C20: Other transformations of harmonic type
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 198
• Numer: 2
• Strony: 197-206

Daty

wydano

2010

Twórcy

autor

Martin Grigoryan

• Yerevan State University, 0025 Yerevan, Armenia

Identyfikatory

DOI

10.4064/sm198-2-6