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A nonlinear Tauberian theorem in function theory


Author: Albert Baernstein
Journal: Trans. Amer. Math. Soc. 146 (1969), 87-105
MSC: Primary 30.57
DOI: https://doi.org/10.1090/S0002-9947-1969-0257358-3
MathSciNet review: 0257358
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  • [1] David Drasin, Tauberian theorems and slowly varying functions, Trans. Amer. Math. Soc. 133 (1968), 333-356. MR 0226017 (37:1607)
  • [2] A. Edrei and W. H. J. Fuchs, The deficiencies of meromorphic functions of order less than one, Duke Math. J. 27 (1960), 233-250. MR 0123717 (23:A1039)
  • [3] -, Bounds for the number of deficient values of certain classes of meromorphic functions, Proc. London Math. Soc. 12 (1962), 315-344. MR 0138765 (25:2208)
  • [4] -, ``Tauberian theorems for a class of meromorphic functions with negative zeros and positive poles,'' in Contemporary problems in the theory of analytic functions, (Internat. Conference in Function Theory, Erevan, 1965), Izdat. ``Nauka", Moscow, 1966, pp. 339-358. MR 0213561 (35:4421)
  • [5] -, Valeurs déficientes et valeurs asymptotiques des fonctions meromorphes, Comment. Math. Helv. 34 (1960), 258-295. MR 0123716 (23:A1038)
  • [6] W. Feller, An introduction to probability theory and its applications, Vol. II, Wiley, New York, 1966. MR 0210154 (35:1048)
  • [7] G. H. Hardy, Divergent series, Oxford Univ. Press, Oxford, 1949. MR 0030620 (11:25a)
  • [8] W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964. MR 0164038 (29:1337)
  • [9] S. Hellerstein and D. F. Shea, Bounds for the deficiencies of meromorphic functions of finite order, Proc. Sympos. Pure Math., Vol. 11, Amer. Math. Soc., Providence, R. I., 1968. MR 0236388 (38:4684)
  • [10] J. Karamata, Sur un mode de croissance régulière des fonctions, Mathematica (Cluj) 4 (1931), 38-53.
  • [11] R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., Providence, R. I., 1934; reprinted 1967. MR 1451142 (98a:01023)
  • [12] D. F. Shea, On a complement to Valiron's tauberian theorem for the Stieltjes transform, Proc. Amer. Math. Soc. 21 (1969), 1-9. MR 0240505 (39:1852)
  • [13] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959. MR 0114894 (22:5712)
  • [14] G. Valiron, Sur les fonctions entières d'ordre fini et d'ordre nul, et en particulier les fonctions a correspondance régulière, Ann. Fac. Sci. Univ. Toulouse (3) 5 (1913), 117-257. MR 1508338
  • [15] A. Edrei, Sums of deficiencies of meromorphic functions, J. Analyse Math. 14 (1965), 79-107. MR 0180678 (31:4909)

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DOI: https://doi.org/10.1090/S0002-9947-1969-0257358-3
Article copyright: © Copyright 1969 American Mathematical Society

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