Abstract:
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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