Geodesic
Extension Theorem of Whitney Type for $\mathcal S(\mathbb{R}_+^d)$ by Use of The Kernel Theorem
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 59

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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 $\mathcal{S}(\mathbb{R}_+^d)$.
DOI : 10.2298/PIM1613059J
Classification : 46F05
Keywords: tempered distributions on $\mathbb{R}^d_+$, kernel theorem for tempered distributions on $\mathbb{R}^d_+$, smooth extensions of smooth rapidly decreasing functions 
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     title = {Extension {Theorem} of {Whitney} {Type} for $\mathcal S(\mathbb{R}_+^d)$ by {Use} of {The} {Kernel} {Theorem}},
     journal = {Publications de l'Institut Math\'ematique},
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Smiljana Jakšić; Bojan Prangoski. Extension Theorem of Whitney Type for $\mathcal S(\mathbb{R}_+^d)$ by Use of The Kernel Theorem. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 59 . doi: 10.2298/PIM1613059J

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