A Generalization of the Fourier-Borel Transformation for the Analytic Functionals with non Convex Carrier
1979; Publication Committee for the Tokyo Journal of Mathematics; Volume: 2; Issue: 2 Linguagem: Inglês
10.3836/tjm/1270216325
ISSN0387-3870
Autores Tópico(s)Functional Equations Stability Results
ResumoIfixed complex number.For $\tau\in P'(K)$ , we define the transformationThis simple transformation $\mathscr{J}_{\lambda}$ generalizes the Fourier-Borel transformation in the case of annulus and we can determine the image of $d'(K)$ under the transformation $F_{\lambda}$ (Theorem 4.2). (Kiselman [4] and Martineau [7] considered another kind of generalizations of the Fourier- Borel transformation.)On the other hand, let $S^{r\iota-1}$ be the $n-1$ dimensional sphere and $\mathscr{G}(S^{n-1})=\mathscr{A}'(S^{-1})$ the space of hyperfunctions (analytic functionals) on the sphere.For $\tau\in \mathscr{B}(S^{n-1})$ , Hashizume, Kowata, Minemura and Oka- moto [2] defined the transformation $\ovalbox{\tt\small REJECT}_{\lambda}$ by (0.3) $\ovalbox{\tt\small REJECT}_{\lambda}(T)(x)=\langle T_{\omega}, \exp(i\lambda\langle x, \omega\rangle)\rangle$ .
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