摘要：We establish some properties of iterations of the remainder operator which assigns to any convergent series the sequence of its remainders. Moreover, we introduce the spaces of multiple absolute summable sequences. We also present some tests for multiple absolute convergence of series. These tests extend the well-known classical tests for absolute convergence of series. For example we generalize the Raabe, Gauss, and Bertrand tests. Next we present some applications of our results to the study of asymptotic properties of solutions of difference equations. We use the spaces of multiple absolute summable sequences as the measure of approximation. MSC:39A10.
关键词：remainder operator ; Raabe’s test ; Gauss’s test ; Bertrand’s test ; difference equation ; prescribed asymptotic behavior ; asymptotically polynomial solution
