Extension Theorem of Whitney Type for $\mathcal S(\mathbb{R}_+^d)$ by Use of The Kernel Theorem

Smiljana Jakšić, Bojan Prangoski

We study the expansions of the elements in $\mathcal S(\mathbb{R}_+^d)$ and $\mathcal{S}'(\mathbb{R}_+^d)$ with respect to the Laguerre orthonormal basis, extending the result of M. Guillemot-Teissier in the one dimensional case. As a consequence, we obtain Kernel theorem for $\mathcal{S}(\mathbb{R}_+^d)$ and $\mathcal{S}'(\mathbb{R}_+^d)$ and an extension theorem of Whitney type for $\mathcal{S}(\mathbb{R}_+^d)$.