LIOUVILLE TYPE THEOREM FOR SOLUTIONS OF INFRA-EXPONENTIAL GROWTH OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS
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概要
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We discuss existence of global solutions of infra-exponential growth to a linear partial differential equation with constant coefficients whose total symbol P(ζ) has the origin as its only real zero. We show that such a solution necessarily reduces to an entire infra-exponential function if and only if the complex zeros of P(ζ) is absent in a strip |Imζ|<δ, |Reζ|>1/δ. This is a generalization of Schwartz's theorem, which in turn generalizes the classical Liouville theorem in the theory of functions.
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著者
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Kaneko Akira
Department Of Information Sciences Ochanomizu University
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Kaneko Akira
Department Of Agricultrural Chemistry And Department Of Forestry Faculty Of Agriculture Ehime Univer
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