TY - JOUR UR - http://lib.ugent.be/catalog/pug01:8159733 ID - pug01:8159733 LA - eng TI - Eigenfunction expansions of ultradifferentiable functions and ultradistributions in ℝⁿ PY - 2016 JO - (2016) JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS SN - 1662-9981 PB - 2016 AU - Vuckovic, Dorde UGent 000141238565 802002000357 802002005613 AU - Vindas Diaz, Jasson WE01 802000645185 0000-0002-3789-8577 AB - We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb{R}^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb{R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of decay estimates for the Fourier coefficients of their elements with respect to eigenfunction expansions associated to normal globally elliptic differential operators of Shubin type. Moreover, we show that the eigenfunctions of such operators are absolute Schauder bases for these spaces of ultradifferentiable functions. Our characterization extends earlier results by Gramchev et al. (Proc. Amer. Math. Soc. 139 (2011), 4361--4368) for Gevrey weight sequences. It also generalizes to $\mathbb{R}^{n}$ recent results by Dasgupta and Ruzhansky which were obtained in the setting of compact manifolds. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 8159733 | ||
005 | 20180816075744.0 | ||
008 | 161120s2016------------------------eng-- | ||
022 | a 1662-9981 | ||
024 | a 000386622500005 2 wos | ||
024 | a 1854/LU-8159733 2 handle | ||
024 | a 10.1007/s11868-016-0157-9 2 doi | ||
040 | a UGent | ||
245 | a Eigenfunction expansions of ultradifferentiable functions and ultradistributions in ℝⁿ | ||
260 | c 2016 | ||
520 | a We obtain a characterization of ${\mathcal S}^{\{M_p\}}_{\{M_p\}}(\mathbb{R}^n)$ and $\mathcal {S}^{(M_p)}_{(M_p)}(\mathbb{R}^n)$, the general Gelfand-Shilov spaces of ultradifferentiable functions of Roumieu and Beurling type, in terms of decay estimates for the Fourier coefficients of their elements with respect to eigenfunction expansions associated to normal globally elliptic differential operators of Shubin type. Moreover, we show that the eigenfunctions of such operators are absolute Schauder bases for these spaces of ultradifferentiable functions. Our characterization extends earlier results by Gramchev et al. (Proc. Amer. Math. Soc. 139 (2011), 4361--4368) for Gevrey weight sequences. It also generalizes to $\mathbb{R}^{n}$ recent results by Dasgupta and Ruzhansky which were obtained in the setting of compact manifolds. | ||
598 | a A1 | ||
100 | a Vuckovic, Dorde u UGent 0 000141238565 0 802002000357 0 802002005613 0 972855541267 | ||
700 | a Vindas Diaz, Jasson u WE01 0 802000645185 0 0000-0002-3789-8577 | ||
650 | a Mathematics and Statistics | ||
653 | a eigenfunction expansions | ||
653 | a Shubin type differential operators | ||
653 | a Gelfand-Shilov spaces | ||
653 | a ultradifferentiable functions | ||
653 | a ultradistributions | ||
653 | a Denjoy-Carleman classes | ||
653 | a SPACES | ||
773 | t JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS g J. Pseudo-Differ. Oper. Appl. 2016. 7 (4) p.519-531 q 7:4<519 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/8159733/file/8159894 z [open] y Vuckovic__D.__Vindas__J.__Eigenfunctionexpansions_of_ultradifferentiable_functions_and_ultradistributions_in_R_n.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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