Geodesic
Pseudodifference operators and uniform convergence of
Sbornik. Mathematics, Tome 193 (2002) no. 2, pp. 205-230

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The concept of pseudodifference operator is introduced. The properties of a class of pseudodifference operators in spaces of fractional quotients are studied. A local theorem on the uniform convergence of divided differences of arbitrary order for an approximate solution is established. In particular, the local infinite differentiability of a precise solution of operator equations of elliptic type with locally infinitely differentiable right-hand side is proved on the basis of a numerical method. Examples related to applications are presented. 
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     author = {I. K. Lifanov and L. N. Poltavskii},
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I. K. Lifanov; L. N. Poltavskii. Pseudodifference operators and uniform convergence of. Sbornik. Mathematics, Tome 193 (2002) no. 2, pp. 205-230. http://geodesic.mathdoc.fr/item/SM_2002_193_2_a2/