Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Uniform approximation on unbounded sets by harmonic functions with logarithmic singularities

Authors: P. M. Gauthier, M. Goldstein and W. H. Ow
Journal: Trans. Amer. Math. Soc. 261 (1980), 169-183
MSC: Primary 30E10; Secondary 31C05
MathSciNet review: 576870
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper deals with the qualitative theory of uniform approximation by harmonic functions. The theorems of Brelot and Deny on Runge- and Walsh-type approximation on compact sets are extended to unbounded closed sets.

References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Fortsetzung Riemannscher Flächen, Math. Ann. 98 (1928), no. 1, 406–421 (German). MR 1512413,
  • [2] M. Brelot, Sur l’approximation et la convergence dans la théorie des fonctions harmoniques ou holomorphes, Bull. Soc. Math. France 73 (1945), 55–70 (French). MR 0013824
  • [3] Jacques Deny, Systèmes totaux de fonctions harmoniques, Ann. Inst. Fourier Grenoble 1 (1949), 103–113 (1950) (French). MR 0037414
  • [4] P. M. Gauthier, Meromorphic uniform approximation on closed subsets of open Riemann surfaces, Approximation theory and functional analysis (Proc. Internat. Sympos. Approximation Theory, Univ. Estadual de Campinas, Campinas, 1977) North-Holland Math. Stud., vol. 35, North-Holland, Amsterdam-New York, 1979, pp. 139–158. MR 553419
  • [5] P. M. Gauthier and W. Hengartner, Approximation sur les fermés par des fonctions analytiques sur une surface de Riemann, C. R. Acad. Bulgare Sci. 26 (1973), 731–732 (French). MR 0340611
  • [6] L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. MR 0261018
  • [7] N. S. Landkof, Foundations of modern potential theory, Springer-Verlag, New York-Heidelberg, 1972. Translated from the Russian by A. P. Doohovskoy; Die Grundlehren der mathematischen Wissenschaften, Band 180. MR 0350027
  • [8] Albert Pfluger, Theorie der Riemannschen Flächen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0084031
  • [9] Arnaud de la Pradelle, Approximation et caractère de quasi-analyticité dans la théorie axiomatique des fonctions harmoniques, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 1, 383–399 (French). MR 0227456
  • [10] Alice Roth, Uniform and tangential approximations by meromorphic functions on closed sets, Canad. J. Math. 28 (1976), no. 1, 104–111. MR 0470220,
  • [11] A. A. Šaginjan, The uniform and tangent harmonic approximation of continuous functions on arbitrary sets, Mat. Zametki 9 (1971), 131–142 (Russian). MR 0293298
  • [12] Stephen Scheinberg, Uniform approximation by functions analytic on a Riemann surface, Ann. of Math. (2) 108 (1978), no. 2, 257–298. MR 0499183,

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30E10, 31C05

Retrieve articles in all journals with MSC: 30E10, 31C05

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society