This is a continuation of an earlier paper [Inventiones Math., 8 (1969), 175-221]. It is assumed that a space and a sheaf over are given, such that the pair 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 does not admit a global potential (in particular, the case where is compact). 2) Construction of a new fine resolution of the sheaf , in which is a (complete pre-)sheaf of measures on . 3) Construction of a natural duality between the flux functional corresponds to a distinguished positive element of .
Cet article est la suite d’une publication antérieure [Inventiones Math., 8 (1969), 175-221]. On développe, à partir d’un espace et d’un faisceau 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 n’admet pas de potentiel global (cas particulier : compact). 2) La construction d’une nouvelle résolution fine de , étant un faisceau naturel de mesures sur . 3) La construction d’une dualité naturelle entre et ( supports compacts), faisant correspondre le flux à un élément positif distingué de .
@article{AIF_1969__19_2_371_0, 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/} }
TY - JOUR TI - Flux in axiomatic potential theory. II. Duality JO - Annales de l'Institut Fourier PY - 1969 DA - 1969/// SP - 371 EP - 417 VL - 19 IS - 2 PB - Imprimerie Durand PP - 28 - Luisant UR - https://aif.centre-mersenne.org/articles/10.5802/aif.331/ UR - https://zbmath.org/?q=an%3A0181.11703 UR - https://www.ams.org/mathscinet-getitem?mr=42 #2023 UR - https://doi.org/10.5802/aif.331 DO - 10.5802/aif.331 LA - en ID - AIF_1969__19_2_371_0 ER -
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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