Frank, Rupert and Sukochev, Fedor and Zanin, Dmitriy (2023) Asymptotics of singular values for quantum derivatives. Transactions of the American Mathematical Society, 376 (3). pp. 2047-2088. ISSN 0002-9947. doi:10.1090/tran/8827. https://resolver.caltech.edu/CaltechAUTHORS:20230124-11595100.7
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Abstract
We obtain Weyl type asymptotics for the quantised derivative \dj ƒ of a function ƒ from the homgeneous Sobolev space Ẇ^(1)_(d) on (ℝᵈ). The asymptotic coefficient ||∇ƒ||_[L_(d)(ℝᵈ)] is equivalent to the norm of \dj ƒ in the principal ideal L_(d,∞), thus, providing a non-asymptotic, uniform bound on the spectrum of \dj ƒ. Our methods are based on the C*-algebraic notion of the principal symbol mapping on ℝᵈ, as developed recently by the last two authors and collaborators.
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| Additional Information: | This work was partially supported through U.S. National Science Foundation grant DMS-1954995 and through the German Research Foundation grant EXC-2111-390814868 (R.L.F.). | ||||||
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| Issue or Number: | 3 | ||||||
| DOI: | 10.1090/tran/8827 | ||||||
| Record Number: | CaltechAUTHORS:20230124-11595100.7 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20230124-11595100.7 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 118915 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Research Services Depository | ||||||
| Deposited On: | 17 Feb 2023 20:09 | ||||||
| Last Modified: | 21 Feb 2023 17:35 |
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