On finite discrete operators and equations

For discrete operators generated by Calderon–Zygmund kernels we consider certain finite-dimensional approximations. We compare an initial discrete operator with its finite-dimensional analogue and obtain invertibility conditions and approximation rate. The error estimate for approximate finite-dimensional solution of corresponding equation is given also for a special right-hand side. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)