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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On semiregular points of the Martin boundary
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by Aurel Cornea and Peter A. Loeb PDF
Proc. Amer. Math. Soc. 103 (1988), 117-124 Request permission

Abstract:

For a selfadjoint, Brelot harmonic space with Martin boundary, call "semiregular" a point $z$ of the boundary at which the Green function has a positive upper limit; call "maximal" the filter ${\mathcal {F}_z}$ converging to $z$ along which that upper limit is attained. If such a $z$ is minimal then any bounded harmonic function has a limit along ${\mathcal {F}_z}$ and ${\mathcal {F}_z}$ is coarser than the fine filter associated with $z$. The semiregular points form a set of harmonic measure zero.
References
  • Alano Ancona, Une propriété de la compactification de Martin d’un domaine euclidien, Ann. Inst. Fourier (Grenoble) 29 (1979), no. 4, ix, 71–90 (French, with English summary). MR 558589
  • Heinz Bauer, Šilovscher Rand und Dirichletsches Problem, Ann. Inst. Fourier (Grenoble) 11 (1961), 89–136, XIV (German, with French summary). MR 136983
    • J. Bliedtner and P. A. Loeb, Simplicial compactifications (to appear).
  • Nicu Boboc, Gheorghe Bucur, and Aurel Cornea, Order and convexity in potential theory: $H$-cones, Lecture Notes in Mathematics, vol. 853, Springer, Berlin, 1981. In collaboration with Herbert Höllein. MR 613980
  • N. Boboc and A. Cornea, Convex cones of lower semicontinuous functions on compact spaces, Rev. Roumaine Math. Pures Appl. 12 (1967), 471–525. MR 216278
  • M. Brelot, Lectures on potential theory, Lectures on Mathematics, vol. 19, Tata Institute of Fundamental Research, Bombay, 1960. Notes by K. N. Gowrisankaran and M. K. Venkatesha Murthy. MR 0118980
  • Marcel Brelot, On topologies and boundaries in potential theory, Lecture Notes in Mathematics, Vol. 175, Springer-Verlag, Berlin-New York, 1971. Enlarged edition of a course of lectures delivered in 1966. MR 0281940
  • Aurel Cornea, Sur la dénombrabilité à l’infini d’un espace harmonique de Brelot, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A190–A191 (French). MR 206321
  • Richard A. Hunt and Richard L. Wheeden, Positive harmonic functions on Lipschitz domains, Trans. Amer. Math. Soc. 147 (1970), 507–527. MR 274787, DOI 10.1090/S0002-9947-1970-0274787-0
  • Teruo Ikegami, Compactifications of Martin type of harmonic spaces, Osaka J. Math. 23 (1986), no. 3, 653–680. MR 866270
  • Peter A. Loeb, A regular metrizable boundary for solutions of elliptic and parabolic differential equations, Math. Ann. 251 (1980), no. 1, 43–50. MR 583823, DOI 10.1007/BF01420279
    • L. Naïm (= L. Lumer-Naïm), Sur le rôle de la frontière de R. S. Martin dans la théorie du potentiel, Ann. Inst. Fourier (Grenoble) 7 (1957), 183-281.
  • M. G. Šur, A Martin compactum with a non-negligible irregular boundary point, Teor. Verojatnost. i Primenen. 17 (1972), 366–370 (Russian, with English summary). MR 0301219
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 117-124
  • MSC: Primary 31D05; Secondary 31C35
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0938654-8
  • MathSciNet review: 938654