Abstract:
The theory of spaces of fractional quotients is expounded. These are, essentially, discrete analogues of the Sobolev-Slobodetskii spaces. They have been devised for a mathematical substantiation of the method of closed discrete vortex frameworks in the numerical solution of problems relating to flows of an ideal incompressible fluid about bodies in space.
Citation:
I. K. Lifanov, L. N. Poltavskii, “Spaces of fractional quotients, discrete operators, and their applications. I”, Sb. Math., 190:9 (1999), 1267–1323
This publication is cited in the following 7 articles:
V. B. Vasilyev, O. A. Tarasova, “On Discrete Boundary-Value Problems and Their Approximation Properties”, J Math Sci, 272:5 (2023), 634
V. B. Vasilev, O. A. Tarasova, “O diskretnykh kraevykh zadachakh i ikh approksimatsionnykh svoistvakh”, Geometriya i mekhanika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 12–19
Lifanov I.K., Poltavskii L.N., “Spaces of fractional quotients of periodic functions”, Differ. Equ., 39:5 (2003), 726–749
I. K. Lifanov, L. N. Poltavskii, “Pseudodifference operators and uniform convergence of
divided differences”, Sb. Math., 193:2 (2002), 205–230
A. Yu. Anfinogenov, I. K. Lifanov, P. I. Lifanov, “On certain one- and two-dimensional hypersingular integral equations”, Sb. Math., 192:8 (2001), 1089–1131
Anfinogenov, AY, “Numerical solution of a hypersingular integral equation in the Neumann problem for the Laplace equation on a sphere and a torus”, Doklady Mathematics, 63:3 (2001), 322
I. K. Lifanov, L. N. Poltavskii, “Spaces of fractional quotients, discrete operators, and their applications. II”, Sb. Math., 190:11 (1999), 1623–1687
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