Tauberian conditions under which convergence follows from Cesàro summability of double integrals over R2
Tauberian conditions under which convergence follows from Cesàro summability of double integrals over R2
For a real- or complex-valued continuous function f over R2+:= [0,1) x [0,1), we denote its integral over [0,u] x [0,v] by s(u,v) and its (C,1, 1) mean, the average of s(u,v) over [0,u] x [0,v], by σ(u,v). The other means (C,1,0) and (C; 0; 1) are defined analogously. We …