no. 1
A maximal regular boundary for solutions of elliptic differential equations
Annales de l'Institut Fourier, Tome 18 (1968) no. 1, pp. 283-308.

Soit 𝒜 une classe harmonique de Brelot, définie sur W. Il est donné un critère de régularité en termes de barrières, pour les points d’une frontière idéale. Soit ℌ un sous-treillis banachique de ℬ𝒜 W . Si 𝒜 est hyperbolique, la frontière idéale compactifiante déterminée par ℌ contient une “frontière harmonique” Γ ℌ qui satisfait le critère de régularité et ℌ≅𝒞 R (Γ ℌ ). Entre autres applications, on a la théorie des frontières de Wiener et Royden et des comparaisons de classes harmoniques.

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     title = {A maximal regular boundary for solutions of elliptic differential equations},
     journal = {Annales de l'Institut Fourier},
     pages = {283--308},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {18},
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Loeb, Peter; Walsh, Bertram. A maximal regular boundary for solutions of elliptic differential equations. Annales de l'Institut Fourier, Tome 18 (1968) no. 1, pp. 283-308. doi : 10.5802/aif.284. http://www.numdam.org/articles/10.5802/aif.284/

[1] M. Brelot, Lectures on Potential Theory, Tata Inst. of Fundamental Research, Bombay, 1960. | MR | Zbl

[2] C. Constantinescu and A. Cornea, Ideale Ränder Riemannscher Flächen, Ergebnisse der Math. (2) 32 (1963). | MR | Zbl

[3] C. Constantinescu and A. Cornea, Compactifications of harmonic spaces, Nagoya Math. J. 25 (1965), 1-57. | MR | Zbl

[4] S. Kakutani, Concrete representation of abstract (M)-spaces, Ann. of Math. (2) 42 (1941), 994-1024. | MR | Zbl

[5] P.A. Loeb, An axiomatic treatment of pairs of elliptic differential equations, Ann. Inst. Fourier (Grenoble) 16,2 (1966), 167-208. | EuDML | Numdam | MR | Zbl

[6] P.A. Loeb, A minimal compactification for extending continuous functions, Proc. Amer. Math. Soc. 18,2 (1967), 282-283. | MR | Zbl

[7] P.A. Loeb and B. Walsh, The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot, Ann. Inst. Fourier (Grenoble) 15 (1965), 597-600. | EuDML | Numdam | MR | Zbl

[8] L. Lumer-Naïm, Harmonic product and harmonic boundary for bounded complex-valued harmonic functions, Abstract 623-18, Notices Amer. Math. Soc. 12 (1965), 355.

[9] I.E. Segal, Decompositions of operator algebras, I, Memoirs Amer. Math. Soc. 9 (1951). | MR | Zbl

[10] J.C. Taylor, The Feller and Šilov boundaries of a vector lattice, Illinois J. Math. 10 (1966), 680-693. | MR | Zbl

[11] B. Walsh and P.A. Loeb, Nuclearity in axiomatic potential theory, Bull. Amer. Math. Soc. 72 (1966), 685-689. | MR | Zbl

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