Frames of solutions and discrete analysis of pseudo‐differential equations

We construct discrete analogs of multidimensional singular integral operators and study their invertibility. Moreover, we give a comparison between continual case. the theory periodic Riemann problem also, because it is needed for studying invertibility so-called paired equations. For more general case pseudo-differential operators, solvability equations in Sobolev–Slobodetskii spaces. Some results continuous solutions are given also appropriate normed