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- Title
Frames of solutions and discrete analysis of pseudo‐differential equations.
- Authors
Vasilyev, Alexander V.; Vasilyev, Vladimir B.; Tarasova, Oksana A.
- Abstract
We construct discrete analogs of multidimensional singular integral operators and study their invertibility. Moreover, we give a comparison between continual and discrete case. We give the theory of periodic Riemann problem also, because it is needed for studying invertibility of so‐called paired equations. For more general case of pseudo‐differential operators, we construct the solvability theory for discrete pseudo‐differential equations in discrete analogs of Sobolev–Slobodetskii spaces. Some comparison results for discrete and continuous solutions are given also in appropriate discrete normed spaces.
- Subjects
PSEUDODIFFERENTIAL operators; RIEMANN-Hilbert problems; NORMED rings; INTEGRAL operators; EQUATIONS
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 10, p8042
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.8159