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A notion of boundedness for hyperfunctions and Massera type theorems

100%

Okada Y.

Banach Center Publications

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2012

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tom 97

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nr 1

101-111

EN

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.

2

The micro-support of the complex defined by a convolution operator in tube domains

63%

Ishimura R., Okada Y.

Banach Center Publications

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1996

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tom 33

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nr 1

105-114

3

Continuation of holomorphic solutions to convolution equations in complex domains

51%

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

Annales Polonici Mathematici

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2000

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tom 74

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nr 1

105-115

EN

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.

Ograniczanie wyników

2 Banach Center Publications

1 Annales Polonici Mathematici

3 Okada Y.

2 Ishimura R.

1 Okada J.-i.

1 2012

1 2000

1 1996

A notion of boundedness for hyperfunctions and Massera type theorems

The micro-support of the complex defined by a convolution operator in tube domains

Continuation of holomorphic solutions to convolution equations in complex domains