Geodesic
Averaging technique in the periodic decomposition problem
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 184-195 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $T_1$, $T_2$ be a pair of commuting isometries in a Banach space $X$. Generalizing results of M. Laczkovich and Sz. Revesz we prove that in many cases element $x$ of $\mathrm{Ker}[(I-T_1)(I-T_2)]$ can be decomposed as a sum $x_1+x_2$ where $x_k\in\mathrm{Ker}(I-T_k)$, $k=1,2$. Moreover, using an averaging technique we prove the existence of linear operators perfoming such a representation. The results are applicable for decomposition of functions into a sum of periodic ones. 
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     author = {V. M. Kadets and B. M. Shumyatskiy},
     title = {Averaging technique in the periodic decomposition problem},
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     pages = {184--195},
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     language = {en},
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}
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V. M. Kadets; B. M. Shumyatskiy. Averaging technique in the periodic decomposition problem. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 2, pp. 184-195. http://geodesic.mathdoc.fr/item/JMAG_2000_7_2_a3/