On modified Borel methods
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- by Dieter Gaier
- Proc. Amer. Math. Soc. 6 (1955), 873-879
- DOI: https://doi.org/10.1090/S0002-9939-1955-0074549-0
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References
- R. P. Boas, Jr., Entire functions, New York, 1954.
M. L. Cartwright, On certain integral functions of order $1$, Quart. J. Math. Oxford Ser. vol. 7 (1936) pp. 46-55.
G. Doetsch, Eine neue Verallgemeinerung der Borelschen Summabilitätstheorie der divergenten Reihen, Dissertation, Göttingen, 1920.
—, Handbuch der Laplace-Transformation I, Basel, 1950.
- R. J. Duffin and A. C. Schaeffer, Power series with bounded coefficients, Amer. J. Math. 67 (1945), 141–154. MR 11322, DOI 10.2307/2371922
- Dieter Gaier, Zur Frage der Indexverschiebung beim Borel-Verfahren, Math. Z. 58 (1953), 453–455 (German). MR 57352, DOI 10.1007/BF01174160 —, On the change of index for summable series, to appear in Pacific Journal of Mathematics.
- G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620 A. J. Macintyre, Laplace’s transformation and integral functions, Proc. London Math. Soc. (2) vol. 45 (1938-1939) pp. 1-20.
- W. Meyer-König, Untersuchungen über einige verwandte Limitierungsverfahren, Math. Z. 52 (1949), 257–304 (German). MR 32021, DOI 10.1007/BF02230694
- W. Meyer-König and K. Zeller, Über das Taylorsche Summierungsverfahren, Math. Z. 60 (1954), 348–352 (German). MR 62848, DOI 10.1007/BF01187382 A. Pfluger, On analytic functions bounded at the lattice points, Proc. London Math. Soc. (2) vol. 42 (1936-1937) pp. 305-315.
- G. N. Wollan, On Euler methods of summability for double series, Proc. Amer. Math. Soc. 4 (1953), 583–587. MR 56109, DOI 10.1090/S0002-9939-1953-0056109-9
Bibliographic Information
- © Copyright 1955 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 6 (1955), 873-879
- MSC: Primary 40.0X
- DOI: https://doi.org/10.1090/S0002-9939-1955-0074549-0
- MathSciNet review: 0074549