周期函数的保形逼近——结论
Shape preserving approximation of periodic functions -- Conclusion
AI总结：
本文给出周期函数三角多项式共单调逼近的Jackson型估计最终结果，总结保形逼近研究，并指出其与代数多项式情形有本质差异。
摘要：
我们在此给出关于用三角多项式对$2\pi$-周期函数进行共单调逼近时Jackson型估计有效性的最终结果。对于共凸逼近以及所谓的共$q$-单调（$q>2$）逼近，目前所有情况均已明确。因此，本文总结了关于用三角多项式对周期函数进行保形逼近的Jackson型估计的研究。值得注意的是，周期函数的共单调逼近结果与有限区间上连续函数用代数多项式进行共单调逼近的相应结果有本质不同。
英文摘要：
We give here the final results about the validity of Jackson-type estimates in comonotone approximation of $2π$-periodic functions by trigonometric polynomials. For coconvex and the so called co-$q$-monotone, $q>2$, approximations, everything is known by now. Thus, this paper concludes the research on Jackson type estimates of Shape Preserving Approximation of periodic functions by trigonometric polynomials. It is interesting to point out that the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation, by algebraic polynomials, of a continuous function on a finite interval.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
