We present an approach to the study of some normally resolvable differential operators in Sobolev spaces. Within the framework of this approach, we obtain decompositions of some function spaces and, in particular, generalize the Weyl–Helmholtz decomposition. The key role is played by the assertion about the complementability of subspaces of a normed space. Bibliography: 15 titles.
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Translated from Problems in Mathematical Analysis 66, August 2012, pp. 15–38.
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Borovikov, I.A. Normally resolvable operators and direct decompositions of Sobolev spaces. J Math Sci 186, 153–178 (2012). https://doi.org/10.1007/s10958-012-0981-2
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DOI: https://doi.org/10.1007/s10958-012-0981-2