Journal article icon

Journal article

Quantum differentiability of essentially bounded functions on Euclidean space

Abstract:

We investigate the properties of the singular values of the quantised derivatives of essentially bounded functions on R d with d & #x003E;1. The commutator i[sgn(D),1⊗M f ] of an essentially bounded function f on R d acting by pointwise multiplication on L 2 (R d ) and the sign of the Dirac operator D acting on C 2 ⌊d/2⌋ ⊗L 2 (R d ) is called the quantised derivative of f. We prove the condition that the function x↦‖(∇f)(x)‖ 2 d :=((∂ 1 f)(x) 2 +…+(∂ d f)(x) 2 ) d/2 , x∈R d , being integr...

Expand abstract
Publication status:
Published
Peer review status:
Peer reviewed

Actions


Access Document


Files:
Publisher copy:
10.1016/j.jfa.2017.06.020

Authors


More by this author
Institution:
University of Oxford
Division:
SSD
Department:
SOGE
Sub department:
Environmental Change Institute
Role:
Author
Publisher:
Elsevier
Journal:
Journal of Functional Analysis More from this journal
Volume:
273
Issue:
7
Pages:
2353-2387
Publication date:
2017-07-04
Acceptance date:
2017-06-22
DOI:
EISSN:
1096-0783
ISSN:
0022-1236
Keywords:
Pubs id:
pubs:710146
UUID:
uuid:f6510c00-e0e8-467d-af13-7062ba45b5e2
Local pid:
pubs:710146
Source identifiers:
710146
Deposit date:
2018-03-17

Terms of use


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP