Structural theorems for quasiasymptotics of ultradistributions

We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the origin of ultradistributions and discuss connections with Gelfand-Shilov type spaces

Convolutors of translation-modulation invariant Banach spaces of ultradistributions

We study the space of tempered ultradistributions whose convolutions with test functions are all contained in a given translation-modulation invariant Banach space of ultradistributions. Our main result will be the first structural theorem for the aforementioned space. As an application we consider several extensions of convolution.Comment: 37 page

High-frequency issues using rotating voltage injections intended for position self-sensing

The rotor position is required in many control schemes in electrical drives. Replacing position sensors by machine self-sensing estimators increases reliability and reduces cost. Solutions based on tracking magnetic anisotropies through the monitoring of the incremental inductance variations are efficient at low-speed and standstill operations. This inductance can be estimated by measuring the response to the injection of high-frequency signals. In general however, the selection of the optimal frequency is not addressed thoroughly. In this paper, we propose discrete-time operations based on a rotating voltage injection at frequencies up to one third of the sampling frequency used by the digital controller. The impact on the rotation-drive, the computational requirement, the robustness and the effect of the resistance on the position estimation are analyzed regarding the signal frequency

Kernel theorems for Beurling-Bj\"orck type spaces

We prove new kernel theorems for a general class of Beurling-Bj\"orck type spaces. In particular, our results cover the classical Beurling-Bj\"orck spaces $\S^{(\omega)}_{(\eta)}$ and $\S^{\{\omega\}}_{\{\eta\}}$ defined via weight functions $\omega$ and $\eta$.Comment: 17 page