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Abstract  

A characterization formula of an orthonormal multiwavelet with di_erent real dilations and translations for L E 2(R) is presented. The result includes the known result on the classical Hardy space H 2(R).

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Studia Scientiarum Mathematicarum Hungarica
Authors: Jing Quan Chong, Xing Chen Huang, Tuo Yeong Lee, Jing Tao Li, Hui Xiang Sim, Jing Ren Soh, Gabriel Jiaxu Tan, and Jay Kin Heng Tai

We prove that

k=1nsin kθkπθπoπsinttdt+12sinθ+121π0πsinttdt12sin2θ

for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).

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