no. 2
Flux in axiomatic potential theory. II. Duality
Annales de l'Institut Fourier, Volume 19 (1969) no. 2, pp. 371-417.

This is a continuation of an earlier paper [Inventiones Math., 8 (1969), 175-221]. It is assumed that a space W and a sheaf H over W are given, such that the pair (W,H) satisfies the Brelot axioms and also satisfies, locally, the additional hypotheses of the theory of adjoint sheaves. The following subjects are considered: 1) Extension of the adjoint-sheaf theory to the case where (W,H) does not admit a global potential (in particular, the case where W is compact). 2) Construction of a new fine resolution O→H→R→L→O of the sheaf H, in which L is a (complete pre-)sheaf of measures on W. 3) Construction of a natural duality between the flux functional corresponds to a distinguished positive element of H W * .

Cet article est la suite d’une publication antérieure [Inventiones Math., 8 (1969), 175-221]. On développe, à partir d’un espace W et d’un faisceau H défini là-dessus, satisfaisant aux axiomes de Brelot et, localement, aux hypothèses de la théorie des faisceaux adjoints, les sujets suivants : 1) l’extension de la théorie des faisceaux adjoints au cas où (W,H) n’admet pas de potentiel global (cas particulier : W compact). 2) La construction d’une nouvelle résolution fine O→H→R→L→O de H, L étant un faisceau naturel de mesures sur W. 3) La construction d’une dualité naturelle entre Γ(W,H * ) et H K 1 (W,H) (K= supports compacts), faisant correspondre le flux à un élément positif distingué de H W * .

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     author = {Walsh, Bertram},
     title = {Flux in axiomatic potential theory. {II.} {Duality}},
     journal = {Annales de l'Institut Fourier},
     pages = {371--417},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {19},
     number = {2},
     year = {1969},
     doi = {10.5802/aif.331},
     zbl = {0181.11703},
     mrnumber = {42 #2023},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.331/}
}
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Walsh, Bertram. Flux in axiomatic potential theory. II. Duality. Annales de l'Institut Fourier, Volume 19 (1969) no. 2, pp. 371-417. doi : 10.5802/aif.331. https://aif.centre-mersenne.org/articles/10.5802/aif.331/

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