On quantum sobolev inequalities
L Lafleche - Journal of Functional Analysis, 2024 - Elsevier
We investigate the quantum analogue of the classical Sobolev inequalities in the phase
space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators …
space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators …
Convergence of dynamics on inductive systems of Banach spaces
Many features of physical systems, both qualitative and quantitative, become sharply
defined or tractable only in some limiting situation. Examples are phase transitions in the …
defined or tractable only in some limiting situation. Examples are phase transitions in the …
A simple criterion for essential self-adjointness of Weyl pseudodifferential operators
R Fulsche, L van Luijk - arXiv preprint arXiv:2304.07153, 2023 - arxiv.org
We prove new criteria for essential self-adjointness of pseudodifferential operators which do
not involve ellipticity type assumptions. For example, we show that self-adjointness holds in …
not involve ellipticity type assumptions. For example, we show that self-adjointness holds in …
Energy-limited quantum dynamics
L van Luijk - arXiv preprint arXiv:2405.10259, 2024 - arxiv.org
We consider quantum systems with energy constraints. In general, quantum channels and
continuous-time dynamics need not satisfy energy conservation. Physically meaningful …
continuous-time dynamics need not satisfy energy conservation. Physically meaningful …
Heisenberg-smooth operators from the phase space perspective
R Fulsche, L van Luijk - arXiv preprint arXiv:2410.00458, 2024 - arxiv.org
Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory
of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new …
of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new …
Weighted theory of Toeplitz operators on the Fock spaces
J Chen - arXiv preprint arXiv:2501.13571, 2025 - arxiv.org
We study the weighted compactness and boundedness of Toeplitz operators on the Fock
spaces. Fix $\alpha> 0$. Let $ T_ {\varphi} $ be the Toeplitz operator on the Fock space $ F …
spaces. Fix $\alpha> 0$. Let $ T_ {\varphi} $ be the Toeplitz operator on the Fock space $ F …
Commutative Toeplitz algebras and Gelfand theory
MA Rodriguez Rodriguez - 2024 - repo.uni-hannover.de
In this thesis we construct and study commutative Banach and C*-algebras generated by
Toeplitz operators on several function spaces. We begin by introducing Banach algebras …
Toeplitz operators on several function spaces. We begin by introducing Banach algebras …