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Author |
Aliaga, R.J.; Guirao, A.J. |
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Title |
On the preserved extremal structure of Lipschitz-free spaces |
Type |
Journal Article |
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Year |
2019 |
Publication |
Studia Mathematica |
Abbreviated Journal |
Studia Math. |
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Volume |
245 |
Issue |
1 |
Pages |
1-14 |
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Keywords |
concave space; extremal structure; Lipschitz-free space; Lipschitz function; metric alignment; preserved extreme point |
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Abstract |
We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F (X) in terms of simple geometric conditions on the underlying metric space (X, d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p, q in X such that the triangle inequality d (p, q) <= d (p, r) + d (q, r) is uniformly strict for r away from p, q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Holder and countable compacta. |
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Address |
[Aliaga, Ramon J.; Guirao, Antonio J.] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Camino Vera S-N, E-46022 Valencia, Spain, Email: raalva@upvnet.upv.es; |
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Publisher |
Polish Acad Sciences Inst Mathematics-Impan |
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Language |
English |
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ISSN |
0039-3223 |
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Notes |
WOS:000446980500001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
3753 |
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Author |
Bernabeu, J.; Navarro-Salas, J. |
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Title |
A Non-Local Action for Electrodynamics: Duality Symmetry and the Aharonov-Bohm Effect, Revisited |
Type |
Journal Article |
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Year |
2019 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
11 |
Issue |
10 |
Pages |
1191 - 13pp |
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Keywords |
non-local action; electrodynamics; electromagnetic duality symmetry; Aharonov-Bohm effect |
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Abstract |
A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov-Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner. |
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Address |
[Bernabeu, Joan] Ludwig Maximilians Univ Munchen, Phys Dept, Theresienstr 37, D-80333 Munich, Germany, Email: Joan.Bernabeu@physik.uni-muenchen.de; |
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Mdpi |
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English |
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Notes |
WOS:000495457600005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4192 |
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Permanent link to this record |