期刊文献+

基于PBV条件下正弦与余弦积分的收敛性

Convergence of Sine and Cosine Integrals under PBV Condition
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摘要 基于文献[2]中的思想,将系数数列的PBV条件推广到函数的PBV条件,分别给出了PBV条件下正弦积分与余弦积分一致收敛性的充分必要条件(见定理1和定理2),并利用Cauchy收敛准则、分部积分等一些数学技巧去证明,最后给出了PBV条件中一个性质不可缺少的例子。 This paper promotes PBV condition of coefficient series to PBV condition of function based on the thought in literature [2] and respectively gives necessary and sufficient conditions of uniform convergence of sine and cosine integrals under PBV condition (see theorems 1 and 2); demonstrates them with some mathematical techniques such as Cauchy convergence criterion and integration by parts and finally gives an example of indispensable property in PBV condition.
作者 张静
出处 《浙江理工大学学报(自然科学版)》 2013年第4期620-623,共4页 Journal of Zhejiang Sci-Tech University(Natural Sciences)
关键词 PBV条件 正弦积分 余弦积分 一致收敛性 PBV condition sine integral cosine integral uniform convergence
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  • 1Chaundy T.W.and Jolliffe A.E.,The uniform convergence of a certain class of trigonometric series,Proc.London Math.Soc.,1916,15(2):214-216.
  • 2Leindler L.,On the uniform convergence and boundedness of a certain class of sine series,Anal.Math.,2001,27:279-285.
  • 3Nurcombe J.R.,On the uniform convergence of sine series with quasimonotone coefficients,J.Math.Anal.Appl.,1992,166:577-581.
  • 4Shah S.M.,Trigonometric series with quasi-monotone coefficients,Proc.Amer.Math.Soc.,1962,13:266-273.
  • 5Telyakovskii S.A.,Uniform convergence of trigonometric series with rarely changing coefficients,Math.Notes,2001,70:553-559.
  • 6Xie T.F.and Zhou S.P.,The uniform convergence of certain trigonometric series,J.Math.Anal.Appl.,1994,181:171-180.
  • 7Le R.J.and Zhou S.P.,A new condition for the uniform convergence of certain trigonometric series,Acta Math.Hunqar.,2005,108:161-169.

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