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A notion of boundedness for hyperfunctions and Massera type theorems

100%

Okada Y.

nr 1

101-111

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 recalling the terminology, we briefly review our approach to the equations with finite delay, and announce our recent result on some classes of equations with infinite delay.

Continuation of holomorphic solutions to convolution equations in complex domains

51%

Ishimura R. , Okada J.-i. , Okada Y.

2000

tom 74

nr 1

105-115

For an analytic functional $S$ on $ℂ^n$, we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in $ℂ^n$. We determine the directions in which every solution can be continued analytically, by using the characteristic set.