In this paper we introduce classes of ultradifferentiable functions and the corresponding ultradistributions on ℝ+d, i.e. Gαβ(ℝ+d) and (Gαβ(ℝ+d))′, α,β gt 0, respectively. We give their characterisation through the Laguerre coefficients estimate. Furthermore, we define the modified fractional power of the partial Hankel-Clifford transform and show that this transformation is a topological isomorphism on Gαα(ℝ+d), α≥1. We also investigate the boundedness of the Weyl pseudo-differential operators with symbols from the previously introduced spaces.
TY - CHAP
AU - Jakšić, Smiljana
AU - Pilipović, S.
PY - 2024
UR - https://omorika.sfb.bg.ac.rs/handle/123456789/1473
AB - In this paper we introduce classes of ultradifferentiable functions and the corresponding ultradistributions on ℝ+d, i.e. Gαβ(ℝ+d) and (Gαβ(ℝ+d))′, α,β gt 0, respectively. We give their characterisation through the Laguerre coefficients estimate. Furthermore, we define the modified fractional power of the partial Hankel-Clifford transform and show that this transformation is a topological isomorphism on Gαα(ℝ+d), α≥1. We also investigate the boundedness of the Weyl pseudo-differential operators with symbols from the previously introduced spaces.
PB - Springer Science and Business Media Deutschland GmbH
T2 - Trends in Mathematics
T1 - The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators
EP - 207
SP - 197
VL - 5
DO - 10.1007/978-3-031-57005-6_21
UR - conv_1863
ER -
@inbook{
author = "Jakšić, Smiljana and Pilipović, S.",
year = "2024",
abstract = "In this paper we introduce classes of ultradifferentiable functions and the corresponding ultradistributions on ℝ+d, i.e. Gαβ(ℝ+d) and (Gαβ(ℝ+d))′, α,β gt 0, respectively. We give their characterisation through the Laguerre coefficients estimate. Furthermore, we define the modified fractional power of the partial Hankel-Clifford transform and show that this transformation is a topological isomorphism on Gαα(ℝ+d), α≥1. We also investigate the boundedness of the Weyl pseudo-differential operators with symbols from the previously introduced spaces.",
publisher = "Springer Science and Business Media Deutschland GmbH",
journal = "Trends in Mathematics",
booktitle = "The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators",
pages = "207-197",
volume = "5",
doi = "10.1007/978-3-031-57005-6_21",
url = "conv_1863"
}
Jakšić, S.,& Pilipović, S.. (2024). The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators. in Trends in Mathematics
Springer Science and Business Media Deutschland GmbH., 5, 197-207.
https://doi.org/10.1007/978-3-031-57005-6_21
conv_1863
Jakšić S, Pilipović S. The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators. in Trends in Mathematics. 2024;5:197-207.
doi:10.1007/978-3-031-57005-6_21
conv_1863 .
Jakšić, Smiljana, Pilipović, S., "The Spaces of Ultradistributions Over ℝ+d and the Weyl Calculus of Pseudo-Differential Operators" in Trends in Mathematics, 5 (2024):197-207,
https://doi.org/10.1007/978-3-031-57005-6_21 .,
conv_1863 .
