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Discrete convolution and the integral
Posted:
Jun 18, 1996 7:16 AM


Do you know any literature or articles considering the following or related topics?
Let f be Riemannintegrable 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^(r1). Standard texts on Fractional Calculus do not consider this issue.
Thanks for your help.
Tomi J Laakso University of Helsinki email tomi.laakso@helsinki.fi
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