Extension theorem of Whitney type for $\mathcal S(\mathbb{R}_+^d)$ by the use of the Kernel Theorem

Smiljana Jaksić; Bojan Prangoski

Extension theorem of Whitney type for $\mathcal S(\mathbb{R}_+^d)$ by the use of the Kernel Theorem

Functional Analysis 2016-02-15 v1

Authors: Smiljana Jaksić , Bojan Prangoski

Abstract

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. Guillemont-Teissier in the case $d=1$ . As a consequence, we obtain the Schwartz kernel theorem for $\mathcal{S}(\mathbb{R}_+^d)$ and $\mathcal{S}'(\mathbb{R}_+^d)$ and the extension theorem of Whitney type for $\mathcal{S}(\mathbb{R}_+^d)$ .

Keywords

Schwartz space Laguerre orthonormal basis kernel theorem Whitney extension theorem tempered distributions

Cite

@article{arxiv.1602.04008,
  title  = {Extension theorem of Whitney type for $\mathcal S(\mathbb{R}_+^d)$ by the use of the Kernel Theorem},
  author = {Smiljana Jaksić and Bojan Prangoski},
  journal= {arXiv preprint arXiv:1602.04008},
  year   = {2016}
}

Extension theorem of Whitney type for $\mathcal S(\mathbb{R}_+^d)$ by the use of the Kernel Theorem

Abstract

Keywords

Cite

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