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Abstract
The representation of the Hardy-Lebesque space H2 (Δ) by means of shift operators is used, to find necessary and sufficient conditions for the.singular differential equation zm dy(z)dz + a(z).y(z)=b(z), to have solution in H2 (△). The coefficients a(z) and b(z) are assumed to be locally analytic functions. The case m=2 recovers known results for corresponding problems with analytic solutions in a neighborhood of zero