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数学进展 - 2016, Vol. 45(2): 252-262
研究论文
一类正余弦积分的渐近等式
A Class of Asymptotic Relations for Sine and Cosine Integrals

王柱,冯磊
WANG Zhu, FENG Lei

浙江理工大学理学院, 杭州, 浙江,310018
School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, P. R. China

收稿日期: 2014-06-23
2016, Vol. 45(2): 252-262
DOI: 10.11845/sxjz.2014102b


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摘要 从一类特殊的正余弦级数的渐近和, 以及对三角级数单调性方面的所有研究成果开始, 本文类比离散的情况建立了相应概念,并对一类特殊的正余弦积分的渐近关系进行研究, 得出了一些结论.另外对于文章最后一个定理, 本文得出在极限~$\lim_{t\to\infty}\frac{f(t)}{\omega(t^{-1})}=A$~和连续性模的一些条件下, 除了第二类上确界有界变差函数外,这些推广的单调性概念是等价的.
Abstract:Beginning with the study of a class of asymptotic sums of special sine and cosine series, and the whole research in monotonicity in trigonometric series, some results are built in this article respect to a class of asymptotic formula for some special sine and cosine integrals. Some other concepts of functions are also defined analogous to the study in discrete situations. In the last theorem we states that all the generalized monotonic concepts, except $\mathrm{SBVF}_{2, are equivalent under $\lim_{t\to\infty}\frac{f(t)}{\omega(t^{-1})}=A$ and some assumptions on the modulus of continuity.
PACS:  O174.22  
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[1] 魏明权, 燕敦验. 两类振荡积分算子在混合范空间上的有界性[J]. 数学进展, 2018, 47(1): 71-80.
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