A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $

Mohsen Zivari-Rezapour; Yichen Liu; Behrouz Emamizadeh

doi:10.5802/crmath.520

Équations aux dérivées partielles, Théorie du contrôle

A formula for the sum of

n

weak

^{☆}

closed sets in

L^{\infty}

Mohsen Zivari-Rezapour ¹ ; Yichen Liu ² ; Behrouz Emamizadeh ^3,⁴

¹ Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
² Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
³ Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
⁴ Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1635-1639.

Résumé

In this note, we derive an equation which describes the closure of a particular set comprising $n -$ valued functions. This result provides an answer to a long standing question for which the particular case $n = 2$ had been known and used frequently in the optimal control problems.

Reçu le : 2023-05-15
Révisé le : 2023-05-24
Accepté le : 2023-05-29
Publié le : 2023-11-17

DOI : 10.5802/crmath.520

Classification : 26E40, 49R05
Mots clés : $n-$valued functions, formulation, weak$^\star $ closure, rearrangements, eigenvalues

Affiliations des auteurs :

Mohsen Zivari-Rezapour ¹ ; Yichen Liu ² ; Behrouz Emamizadeh ^{3, 4}

¹ Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
² Department of Applied Mathematics, School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University, Suzhou, China
³ Department of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, China
⁴ Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Mohsen Zivari-Rezapour and Yichen Liu and Behrouz Emamizadeh},
     title = {A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1635--1639},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.520},
     language = {en},
}

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Mohsen Zivari-Rezapour; Yichen Liu; Behrouz Emamizadeh. A formula for the sum of $n$ weak$^\star $ closed sets in $L^\infty $. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1635-1639. doi : 10.5802/crmath.520. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.520/

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