MathDB
Miklos Schweitzer 1966_9

Source:

September 29, 2008
limitreal analysisreal analysis unsolved

Problem Statement

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
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