ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

On the Extreme Points of the Unit Ball in the Space of Solenoidal Vector Measures on the Plane

Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 525--528 | DOI:10.5890/DNC.2020.12.005

Nikolay A. Gusev

Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russia

Abstract

We consider the space of finite divergence-free Borel vector measures on~$\mathbb R^d$, endowed with the total variation norm. For $d=2$ we present a characterization of the extreme points of the unit ball in this space. This allows one to decompose (for $d=2$) any finite divergence-free vector measure into measures induced by closed Lipschitz curves. The results are based on a joint work with P. Bonicatto.

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