Do you know any literature or articles considering the following or related topics?
Let f be Riemann-integrable in [0,oo[. Let f_m be the sequence (f(0),f(1/m),f(2/m),...). Take ANY sequence g and form covolution h_m=g*f_m. Define function k_m(x)=m^(-r) h_m(x/m rounded to integer), where r is positive real number and h_m(i) denotes ith element of h_m. Now it is relatively easy to prove that the operator A_g that send f to lim m->oo k_m is either always divergent or converges to a constant multiple of fractional integral I^(r-1). Standard texts on Fractional Calculus do not consider this issue.
Thanks for your help.
Tomi J Laakso University of Helsinki e-mail email@example.com