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On absolutely convergent exponential sums


Authors: Leon Brown, Allen Shields and Karl Zeller
Journal: Trans. Amer. Math. Soc. 96 (1960), 162-183
MSC: Primary 30.65
DOI: https://doi.org/10.1090/S0002-9947-1960-0142763-8
MathSciNet review: 0142763
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  • [1] S. Banach, Théorie des opérations linéaires, Warszawa-Lwow, 1932.
  • [2] L. Bieberbach, Lehrbuch der Funktionentheorie, vol. II, Leipzig-Berlin, 1927.
  • [3] R. P. Boas, Entire functions, New York, Academic Press, 1954. MR 0068627 (16:914f)
  • [4] M. M. Day, Normed linear spaces, Ergebnisse der Mathematik, vol. 21, Berlin, Springer-Verlag, 1958. MR 0094675 (20:1187)
  • [5] A. Denjoy, Sur les singularités des séries de fractions rationnelles, Rend. Circ. Mat. Palermo vol. 50 (1926) pp. 1-95.
  • [6] -, Sur les séries de fractions rationnelles, Bull. Soc. Math. France vol. 52 (1924) pp. 418-434. MR 1504854
  • [7] Tord Hall, On polynomials bounded at an infinity of points, Thesis, Uppsala, Appelbergs Boktryckeri, 1950. MR 0035862 (12:23e)
  • [8] S. Ya. Havinson, On some extremal problems of the theory of analytic functions, Moscov. Gos. Univ. Uč. Zap. vol. 148 (1951), Matematika vol. 4, pp. 133-143 (Russian). MR 0049322 (14:155f)
  • [9] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, 1957. MR 0089373 (19:664d)
  • [10] E. Landau, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie, 2d ed., 1929.
  • [11] B. Ya. Levin, Distribution of the roots of entire functions, Moscow, 1956 (Russian).
  • [12] A. J. Macintyre and W. W. Rogosinski, Extremum problems in the theory of analytic functions, Acta Math. vol. 82 (1950) pp. 275-325. MR 0036314 (12:89e)
  • [13] S. N. Mergelyan, Uniform approximations to functions of a complex variable, Uspehi Mat. Nauk vol. 7, no. 2 (1952) pp. 31-122; Amer. Math. Soc. Translation, no. 101. MR 0051921 (14:547e)
  • [14] R. Nevanlinna, Eindeutige analytische Funktionen, Berlin, 1936.
  • [15] I. I. Privaloff, Boundary properties of analytic functions, Moscow-Leningrad, 1950 (Russian); Deutscher Verlag der Wissenschaften, Berlin, 1956 (German translation).
  • [16] W. W. Rogosinski and H. S. Shapiro, On certain extremum problems for analytic functions, Acta Math. vol. 90 (1953) pp. 287-318. MR 0059354 (15:516a)
  • [17] J. E. Scroggs, Invariant subspaces of a normal operator, Duke Math. J. vol. 26 (1959) pp. 95-112. MR 0102748 (21:1534)
  • [18] A. E. Taylor, Banach spaces of functions analytic in the unit circle II, Studia Math. vol. 12 (1951) pp. 25-50. MR 0043377 (13:252a)
  • [19] J. L. Walsh, Über die Entwicklung einer analytischen Funktion nach Polynomen, Math. Ann. vol. 96 (1926) pp. 430-436. MR 1512331
  • [20] J. Wermer, On invariant subspaces of normal operators, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 270-277. MR 0048700 (14:55g)
  • [21] J. Wolff, Sur les séries $ \sum {{A_k}/(z - {\alpha _k})} $, C. R. Acad. Sci. Paris vol. 173 (1921) pp. 1057-1058, 1327-1328.

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DOI: https://doi.org/10.1090/S0002-9947-1960-0142763-8
Article copyright: © Copyright 1960 American Mathematical Society

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