This is an extended abstract of a lecture on some results obtained in collaboration with D. Rottensteiner and M. Ruzhansky, which can be found in [3], about the existence of a Weyl calculus on any graded Lie group. Below we will introduce a family of quantizations, the so called τ-quantizations, and present the asymptotic formulas representing the building blocks of the corresponding pseudo-differential symbolic calculus. Then, we will say which one among the τ-quantizations is a Weyl quantization on any graded group. Finally, we will show that the Weyl quantization is uniquely determined in the case of the Heisenberg group ℍn. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025
Federico, S. (2025). On the Existence of a Weyl Calculus on Graded Lie Groups [10.1007/978-3-031-71989-9_1].
On the Existence of a Weyl Calculus on Graded Lie Groups
Federico, Serena
2025
Abstract
This is an extended abstract of a lecture on some results obtained in collaboration with D. Rottensteiner and M. Ruzhansky, which can be found in [3], about the existence of a Weyl calculus on any graded Lie group. Below we will introduce a family of quantizations, the so called τ-quantizations, and present the asymptotic formulas representing the building blocks of the corresponding pseudo-differential symbolic calculus. Then, we will say which one among the τ-quantizations is a Weyl quantization on any graded group. Finally, we will show that the Weyl quantization is uniquely determined in the case of the Heisenberg group ℍn. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
