Images of some functions and functional spaces under the Dunkl-Hermite semigroup

Néjib Ben Salem; Walid Nefzi

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 3, page 345-365
  • ISSN: 0010-2628

Abstract

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We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, 𝒮 ( ℝ ) and L α p ( ℝ ) , 1 < p < ∞ , under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.

How to cite

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Ben Salem, Néjib, and Nefzi, Walid. "Images of some functions and functional spaces under the Dunkl-Hermite semigroup." Commentationes Mathematicae Universitatis Carolinae 54.3 (2013): 345-365. <http://eudml.org/doc/260683>.

@article{BenSalem2013,
abstract = {We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, $\mathcal \{S\}(\mathbb \{R\})$ and $L^p_\alpha (\mathbb \{R\})$, $1<p<\infty $, under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.},
author = {Ben Salem, Néjib, Nefzi, Walid},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space; Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space},
language = {eng},
number = {3},
pages = {345-365},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Images of some functions and functional spaces under the Dunkl-Hermite semigroup},
url = {http://eudml.org/doc/260683},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Ben Salem, Néjib
AU - Nefzi, Walid
TI - Images of some functions and functional spaces under the Dunkl-Hermite semigroup
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 3
SP - 345
EP - 365
AB - We propose the study of some questions related to the Dunkl-Hermite semigroup. Essentially, we characterize the images of the Dunkl-Hermite-Sobolev space, $\mathcal {S}(\mathbb {R})$ and $L^p_\alpha (\mathbb {R})$, $1<p<\infty $, under the Dunkl-Hermite semigroup. Also, we consider the image of the space of tempered distributions and we give Paley-Wiener type theorems for the transforms given by the Dunkl-Hermite semigroup.
LA - eng
KW - Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space; Dunkl-Hermite functions; Dunkl-Hermite semigroup; Dunkl-Hermite-Sobolev space
UR - http://eudml.org/doc/260683
ER -

References

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  10. Rosenblum M., Generalized Hermite polynomials and the Bose-like oscillator calculus, in Operator theory: Advances and Applications, Vol. 73, Birkhäuser, Basel, 1994, pp. 369–396. MR1320555
  11. Rösler M., 10.1007/s002200050307, Comm. Math. Phys. 192 (1998), no. 3, 519–542. MR1620515DOI10.1007/s002200050307
  12. Rösler M., Voit M., 10.1006/aama.1998.0609, Adv. Appl. Math. 21 (1998), 575–643. Zbl0919.60072MR1652182DOI10.1006/aama.1998.0609
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