具有分段有界变差系数的三角级数的一个性质

A Property of Trigonometric Series with Piecewise Bounded Variation Coefficients

将Leindler定理的条件推广到分段有界变差数列(PBVS)中。当正弦级数的Fourier系数满足分段有界变差条件时,结合最佳逼近的定义,运用分段讨论方法,在Lp2π范数下研究得到正弦级数的最佳逼近与Fourier系数之间的关系式,并对关系式进行了证明。

When Fourier coefficient of sine series meets bounded variation condition, this paper gener- alizes the conditions in Leindler theorem to piecewise bounded variation sequence（PBVS）, obtains the rela- tional expression of optimal approximation and coefficient of sine series through research under LP2k norm with piecewise discussion method in combination with the definition of optimal approximation, and proves the formula.