Publications de l'Institut Mathématique, Nouvelle SérieVol. 99(113), pp. 59–65 (2016)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 99(113), pp. 59–65 (2016) |
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EXTENSION THEOREM OF WHITNEY TYPE FOR $\mathcal S(\mathbb{R}_+^d)$ BY USE OF THE KERNEL THEOREMSmiljana Jaksic, Bojan PrangoskiFaculty of Forestry, Belgrade University, Belgrade, Serbia; Faculty of Mechanical Engineering, University Ss. Cyril and Methodius, Skopje, MacedoniaAbstract: 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 $\mathcal{S}(\mathbb{R}_+^d)$. Keywords: tempered distributions on $\mathbb{R}^d_+$; kernel theorem for tempered distributions on $\mathbb{R}^d_+$; smooth extensions of smooth rapidly decreasing functions Classification (MSC2000): 46F05 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.
© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
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