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Asymptotics of singular values for quantum derivatives

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.

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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.

Item Type:Article
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URLURL TypeDescription
Frank, Rupert0000-0001-7973-4688
Sukochev, Fedor0000-0002-6063-3163
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.).
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Issue or Number:3
Record Number:CaltechAUTHORS:20230124-11595100.7
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:118915
Deposited By: Research Services Depository
Deposited On:17 Feb 2023 20:09
Last Modified:21 Feb 2023 17:35

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