| Abstrakt: |
Abstract: In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients $a_{k,l}$ satisfy certain conditions) the following order equality is proved g(x,y)\sim mna_{m,n}+\frac{m}n\sum_{l=1}^{n-1}la_{m,l}+\frac{n}m\sum_{k=1}^{m-1}ka_{k,n}+\frac1{mn}\sum_{l=1}^{n-1}\sum_{k=1}^{m-1}kla_{k,l}, where $x\in(\frac{\pi}{m+1}, \frac{\pi}m]$, $ y\in(\frac{\pi}{n+1}, \frac{\pi}n]$, $ m, n=1,2,\dots$. |
