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Part of 1966 Miklós Schweitzer

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Miklos Schweitzer 1966_9

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9/29/2008
If ∑m=−∞+∞∣am∣<∞ \sum_{m=-\infty}^{+\infty} |a_m| < \infty, then what can be said about the following expression? lim⁡n→∞12n+1∑m=−∞+∞∣am−n+am−n+1+...+am+n∣. \lim_{n \rightarrow \infty} \frac{1}{2n+1} \sum_{m=-\infty}^{+\infty} |a_{m-n}+a_{m-n+1}+...+a_{m+n}|. P. Turan
limitreal analysisreal analysis unsolved