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Expansions of analytic functions


Author: R. P. Boas
Journal: Trans. Amer. Math. Soc. 48 (1940), 467-487
MSC: Primary 30.0X
DOI: https://doi.org/10.1090/S0002-9947-1940-0002594-3
MathSciNet review: 0002594
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  • [1] G. D. Birkhoff, Sur une généralisation de la série de Taylor, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 163 (1917), pp. 942-945.
  • [2] R. F. Graesser, A certain general type of Neumann expansions and expansions in confluent hypergeometric functions, American Journal of Mathematics, vol. 49 (1927), pp. 577-597. MR 1506647
  • [3] S. Izumi, On the expansion of analytic function, Tôhoku Mathematical Journal, vol. 28 (1927), pp. 97-106.
  • [4] G. S. Ketchum, On certain generalizations of the Cauchy-Taylor expansion theory, these Transactions, vol. 40 (1936), pp. 208-224. MR 1501871
  • [5] P. W. Ketchum, Infinite systems of linear equations and expansions of analytic functions, Duke Mathematical Journal, vol. 4 (1938), pp. 668-677. MR 1546087
  • [6] T. Kubota, Eine Verallgemeinerung des Taylor-Cauchyschen Satzes, Tôhoku Mathematical Journal, vol. 22 (1923), pp. 336-347.
  • [7] S. Narumi, A theorem on the expansion of analytic functions, Tôhoku Mathematical Journal, vol. 30 (1929), pp. 441-444.
  • [8] Y. Okada, On a certain expansion of analytic function, Tôhoku Mathematical Journal, vol. 22 (1923), pp. 325-335.
  • [9] S. Pincherle, Sopra alcuni sviluppi in serie per funzioni analitiche, Memorie della Reale Accademia delle Scienze dell'Istituto di Bologna, (4), vol. 3 (1881), pp. 151-180.
  • [10] I. M. Sheffer, Concerning some methods of best approximation, and a theorem of Birkhoff, American Journal of Mathematics, vol. 57 (1935), pp. 587-614. MR 1507098
  • [11] S. Takahashi, On the expansion of analytic function, Proceedings of the Imperial Academy, Tokyo, vol. 6 (1930), pp. 389-392. MR 1568303
  • [12] -, A remark on Mr. D. V. Widder's theorem, Tôhoku Mathematical Journal, vol. 33 (1930), pp. 48-54.
  • [13] -, On the expansion of analytic functions, Tôhoku Mathematical Journal, vol. 35 (1932), pp. 242-243.
  • [14] S. Takenaka, A generalization of Taylor's series, Japanese Journal of Mathematics, vol. 7 (1930), pp. 187-198.
  • [15] -, On the expansion of analytic functions in series of analytic functions and its application to the study of the distribution of zero points of the derivatives of analytic functions, Nippon Sûgaku-Buturigakkwai Kizi (Proceedings of the Physico-Mathematical Society of Japan), (3), vol. 13 (1931), pp. 111-132.
  • [16] L. Tonelli, Sulle serie di funzioni analitiche della forma $ \Sigma {a_n}(x){x^n}$, Annali di Matematica Pura ed Applicata, (3), vol. 18 (1911), pp. 99-103.
  • [17] J. L. Walsh, On the expansion of analytic functions in series of polynomials, these Transactions, vol. 26 (1924), pp. 155-170. MR 1501270
  • [18] -, On the expansion of analytic functions in series of polynomials and in series of other analytic functions, these Transactions, vol. 30 (1928), pp. 307-332. MR 1501430
  • [19] -, Note on the expansion of analytic functions in series of polynomials and in series of other analytic functions, these Transactions, vol. 31 (1929), pp. 53-57. MR 1501467
  • [20] D. V. Widder, On the expansion of analytic functions of a complex variable in generalized Taylor's series, these Transactions, vol. 31 (1929), pp. 43-52. MR 1501466
  • [21] S. Banach, Théorie des Opérations Linéaires, 1932.
  • [22] R. P. Boas, Jr., Univalent derivatives of entire functions, Duke Mathematical Journal, vol. 6 (1940), pp. 719-721. MR 0002601 (2:82b)
  • [23] H. F. Bohnenblust and A. Sobczyk, Extensions of functionals on complex linear spaces, Bulletin of the American Mathematical Society, vol. 44 (1938), pp. 91-93. MR 1563688
  • [24] P. Dienes, The Taylor Series, An Introduction to the Theory of Functions of a Complex Variable, 1931.
  • [25] A. Gelfond, Interpolation et unicité des fonctions entières, Matematicheskii Sbornik (Recueil Mathématique), new series, vol. 4 (1938), pp. 115-147.
  • [26] R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications, vol. 19, 1934. MR 1451142 (98a:01023)
  • [27] G. Pólya, Untersuchungen über Lücken und Singularitäten von Potenzreihen, Mathematische Zeitschrift, vol. 29 (1929), pp. 549-640.
  • [28] I. J. Schoenberg, On the zeros of successive derivatives of integral functions, these Transactions, vol. 40 (1936), pp. 12-23. MR 1501863
  • [29] S. Takenaka, On the expansion of integral transcendental functions in generalized Taylor's series, Nippon Sûgaku-Buturigakkwai Kizi (Proceedings of the Physico-Mathematical Society of Japan), (3), vol. 14 (1932), pp. 529-542.
  • [30] J. M. Whittaker, Interpolatory Function Theory, 1935.
  • [31] A. Zygmund, Trigonometrical Series, 1935.
  • [32] I. I. Ibragimoff (I. Ibraguimoff), Sur quelques systèmes complets de fonctions analytiques (in Russian), Izvestiya Akademii Nauk SSSR, Seriya Matematicheskaya (Bulletin de l'Académie des Sciences de l'URSS, Série Mathématique), 1939, pp. 553-567; French summary, pp. 567-568.

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DOI: https://doi.org/10.1090/S0002-9947-1940-0002594-3
Article copyright: © Copyright 1940 American Mathematical Society

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