@inproceedings{03efd97207cb48729125415fa08ee8d7,
title = "Quantum differentiability – the analytical perspective",
abstract = "The study of quantum differentiability (in the sense of Connes) concerns the characterisation of the singular value sequences of commutators of pointwise multipliers with signs of Dirac operators. This subject ties together several themes in operator theory and harmonic analysis, and is inspired by analytic issues arising from cyclic cohomology and noncommutative differential geometry. We give a unified treatment of some recent results in this area, and a proof of the novel result that the necessary and sufficient conditions for quantum differentiability in noncommutative Euclidean spaces are formally identical to those of commutative Euclidean spaces.",
keywords = "Quantised derivative, Sobolev space, quantum Euclidean spaces, quantum tori, trace formula",
author = "E. McDonald and F. Sukochev and X. Xiong",
note = "Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.; Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 ; Conference date: 27-09-2021 Through 01-10-2021",
year = "2023",
doi = "10.1090/pspum/105/13",
language = "英语",
isbn = "9781470469771",
series = "Proceedings of Symposia in Pure Mathematics",
publisher = "American Mathematical Society",
pages = "257",
editor = "Alain Connes and Alain Connes and Caterina Consani and Dundas, \{Bj{\o}rn Ian\} and Masoud Khalkhali and Henri Moscovici",
booktitle = "Cyclic Cohomology at 40",
address = "美国",
}