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For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains.
In this article, after...
For an analytic functional on , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in . We determine the directions in which every solution can be continued analytically, by using the characteristic set.
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