On the Abstract Cauchy Problems in the Sense of Fourier Hyperfunctions

In this paper we will study the Fourier hyperfunction solution of the abstract Cauchy problem { Jdu(t)/dt = Au(t), u(0) = a, } where A is a closed linear operator in a complex Banach space X and a ∈ X. The abstract Cauchy problem has been studied by many authors ([1], [2], [7], [8], [9] and the others quoted there). By modifying Ouchi's method, our method of using vector valued Fourier hyperfunctions simplifies the necessary and sufficient conditions for the well-posedness of the abstract Cauchy problem in the generalized sense. As for the notions of Fourier hyperfunctions and vector valued Fourier hyperfunctions we refer [3], [4], [5], [6] and [10]. We wish to express our thanks to Professor H. Yoshizawa for his encouragements and to Subprofessor T. Hirai for his encouragements and suggestions during the preparation of this work.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。