Issues:
Sections:
Issue 54
MATHEMATICS AND PHYSICS
UDK: 517.521
APPROXIMATION PROPERTIES OF CLASSIC VALLEE POUSSIN MEANS FOR PIECEWISE SMOOTH FUNCTIONS
MAGOMED-KASUMOV Magomedrasul Grozbekovich
This article is about an appoximation speed of the Vallee Poussin means of trigonometric series for 2π -periodic functions that have a finite number of break points θ i i=1q and on each segment [ θ i , θ i+1 ] they can be turned into the functions from Sobolev space W 13 ( θ i , θ i +1 ) by changing their values on the segment ends. The obtained estimation shows that Vallee Poussin means approximate such functions with 1/ n 2 speed, which is faster than that for the Fourier sums.
Keywords: средние Валле-Пуссена; тригонометрическая система; скорость сходимости; кусочно гладкие функции; аппроксимативные свойства; Vallée Poussin means; trigonometric system; approximation speed; piecewise smooth functions; approximative properties.
Pages: 5 - 11
Date: 23.07.2014
Bibliography:
- Зигмунд А. Тригонометрические ряды / под ред. Н.К. Бари. М.: Мир, 1965. Т. 1. 615 с.
- Фихтенгольц Г.М. Курс дифференциального и интегрального исчисления. М.: Физматлит, 2001. 810 с.