A linear functional equation with a singularity at a fixed point |
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Authors: | V Mityushev |
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Institution: | Institute of Mathematics, Pedagogical College, ul. Arciszewskiego 22B, PL-76-200 Slupsk, Poland, PL
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Abstract: | Summary. Local solutions of the functional equation¶¶zk f( z) = ?k=1nGk( z) f( skz ) +g( z) z{^\kappa} \phi \left( z\right) =\sum_{k=1}^nG_k\left( z\right) \phi \left( s_kz \right) +g\left( z\right) ¶with k > 0 \kappa > 0 and | sk| \gt 1 \left| s_k\right| \gt 1 are considered. We prove that the equation is solvable if and only if a certain system of k \kappa conditions on Gk (k = 1, 2, ... , n) and g is fulfilled. |
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