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- W1567400632 abstract "We characterize the almost periodic hyperfunctions by showing that the following statements are equivalent for any bounded hyperfunction $T$. (i) $T$ is almost periodic. (ii) $T*varphi in C_{ap}$ for every $varphi in mathcal {F}$. (iii) There are two functions $f,g in C_{ap}$ and an infinite order differential operator $P$ such that $T=P(D^{2})f+g.$ (iv) The Gauss transform $u(x,t)=T*E(x,t)$ of $T$ is almost periodic for every $t>0$. Here $C_{ap}$ is the space of almost periodic continuous functions, $mathcal {F}$ is the Sato space of test functions for the Fourier hyperfunctions, and $E(x,t)$ is the heat kernel. This generalizes the result of Schwartz on almost periodic distributions and that of Cioranescu on almost periodic (non-quasianalytic) ultradistributions to the case of hyperfunctions." @default.
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- W1567400632 date "2000-08-30" @default.
- W1567400632 modified "2023-10-16" @default.
- W1567400632 title "Almost periodic hyperfunctions" @default.
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- W1567400632 doi "https://doi.org/10.1090/s0002-9939-00-05800-7" @default.
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