Discrete convolutions and difference equations
by
Vladimir B. Vasilyev
Bryansk State University, Russia

The author developes the theory of pseudodifferential equations and boundary value problems in non-smooth domains. A model pseudodifferential equation in a canonical domain is reduced to a system of linear integral (further difference) equations for which in simplest cases there are certain solution methods. On the other hand the discretization of an initial pseudodifferential equation leads to consideration of corresponding convolutions and necessity of constructing the discrete theory. Both theories have many common points, and in future one takes into account their "diffusion" in a common theory of pseudodifferential equations in non-smooth domains.
1. Vasil'ev V.B. Wave factorization of elliptic symbols: theory and applications. Dordrecht-Boston-London, Kluwer Academic Publishers, 2000.
2. Vasilyev V.B. Fourier multipliers, pseudodifferential equations, wave factorization, boundary value problems. Moscow, Editorial URSS, KomKniga, 2006. (in Russian)

Date received: March 10, 2007