Given a trigonometric polynomial \({T_n}(t) = \sum\nolimits_{k = 1}^n {{\tau _k}\left( t \right),{\tau _k}\left( t \right): = {a_k}\cos kt + {b_k}\sin kt}\) we consider the problem of extracting the sum of harmonics \(\sum \tau_{\mu_s}(t)\) prescribed orders µ_s by the method of amplitude and phase transformations. Such transformations map the polynomials T_n(t) into similar ones using two simple operations: the multiplication by a real constant X and the shift by a real phase λ, i.e., T_n(t) → XT_n(t — λ). We represent the sum of harmonics as a sum of such polynomials and then use this representation to obtain sharp Fejer-type estimates.

中文翻译：

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从三角多项式中提取几个谐波。Fejer型不等式

给定三角多项式\（{T_n}（t）= \ sum \ nolimits_ {k = 1} ^ n {{\ tau _k} \ left（t \ right），{\ tau _k} \ left（t \ right） ：= {a_k} \ cos kt + {b_k} \ sin kt} \）我们考虑通过该方法提取规定阶数_s的谐波和\（\ sum \ tau _ {\ mu_s}（t）\）的问题振幅和相位变换 这种转化映射多项式Ť _Ñ（吨使用两个简单的操作）到类似的：由一个实常数乘法X和由真实相位λ的转变，即，Ť _Ñ（吨）→ XT _Ñ（吨- λ）。我们将谐波总和表示为此类多项式的总和，然后使用该表示形式获得尖锐的Fejer型估计。