Moments and Legendre-Fourier Series for Measures Supported on Curves
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Moments and Legendre-Fourier Series for Measures Supported on Curves
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| Creator |
Lasserre, J.B.
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| Description |
Some important problems (e.g., in optimal transport and optimal control) have a relaxed (or weak) formulation in a space of appropriate measures which is much easier to solve. However, an optimal solution μ of the latter solves the former if and only if the measure μ is supported on a ''trajectory'' {(t,x(t)):t∈[0,T]} for some measurable function x(t). We provide necessary and sufficient conditions on moments (γij) of a measure dμ(x,t) on [0,1]² to ensure that μ is supported on a trajectory {(t,x(t)):t∈[0,1]}. Those conditions are stated in terms of Legendre-Fourier coefficients fj=(fj(i)) associated with some functions fj:[0,1]→R, j=1,…, where each fj is obtained from the moments γji, i=0,1,…, of μ.
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| Date |
2019-02-13T17:42:19Z
2019-02-13T17:42:19Z 2015 |
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| Type |
Article
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| Identifier |
Moments and Legendre-Fourier Series for Measures Supported on Curves / J.B. Lasserre // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 42C05; 42C10; 42A16; 44A60 DOI:10.3842/SIGMA.2015.077 http://dspace.nbuv.gov.ua/handle/123456789/147149 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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