| CHENG NAID0NG.[J].数学年刊A辑,1980,1(2):214~222 |
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| CONSTRUCTIVE PROPERTIES OF A KIND OF UNIFORMLYALMOST PERIODIC FUNCTIONS |
| Received:August 03, 1978 Revised:May 08, 1979 |
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| In this paper,we have discussed constructive properties of a kind of uniformly
almost periodic functions, of which the sequence of its Fourier exponents has unique
limit point at infinity.
\[\begin{gathered}
f(x) \sim \sum\limits_{k = - \infty }^\infty {{A_k}} {e^{i{\Lambda _k}x}} \hfill \ {\Lambda _0} = \alpha ,0 < \alpha \leqslant {\Lambda _k} < {\Lambda _{k + 1}}(k = 0,1,2,...) \hfill \ \mathop {\lim }\limits_{k \to \infty } {\Lambda _k} = \infty ,{\Lambda _k} = - {\Lambda _k} \hfill \ |{\Lambda _k}| + |{\Lambda _{ - k}}| > 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (k \ne 0) \hfill \\
\end{gathered} \]
Analogons to the approximation theory of periodic functioiis, we get some theorems
similar to the Jackson theorem, Bernstein theorem and Zygmund theorem of periodio
functions. |
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