Tauberian theorems and Tauberian conditions
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- by G. G. Lorentz PDF
- Trans. Amer. Math. Soc. 63 (1948), 226-234 Request permission
References
- Ralph Palmer Agnew, Tauberian conditions, Ann. of Math. (2) 42 (1941), 293–308. MR 3266, DOI 10.2307/1968998 G. H. Hardy and J. E. Littlewood, The relations between Borel’s and Cesàro’s methods of summation, Proc. London Math. Soc. vol. 11 (1913) pp. 1-16. —, A further note on the converse of Abel’s theorem, Proc. London Math. Soc. vol. 25 (1926) pp. 219-236. A. E. Ingham, On the “high-indices theorem” of Hardy and Littlewood. Quart. J. Math. Oxford Ser. vol. 8 (1937) pp. 1-7. J. Karamata, Théorèmes inverses de sommabilité I, II, Glas Srpske Kralevske Akad., Beograd, vol. 143 (70) (1931) pp. 3-24, 121-146. —, Sur les théorèmes inverses des procédés de sommabilité, Paris, 1937, 46 pp. E. Landau, Neuere Ergebnisse der Funktionentheorie, 2d ed., Berlin, 1929, 122 pp. J. E. Littlewood, The converse of Abel’s theorem on power series, Proc. London Math. Soc. vol. 9 (1911) pp. 434-443. S. Mazur and W. Orlicz, Sur les méthodes linéaires de sommation, C. R. Acad. Sci. Paris vol. 196 (1933) pp. 32-34. D. Menchoff, Sur une généralisation d’une théorème de M. M. Hardy et Littlewood, Rec. Math. (Mat. Sbornik) N.S. vol. 3 (1938) pp. 367-373; vol. 5 (1939) p. 451. W. Meyer-König, Limitierungsumkehrsätze mit Lückenbedingungen I; II, Math. Zeit, vol. 45 (1939) pp. 447-478; 479-494. H. R. Pitt, General Tauberian theorems, Proc. London Math. Soc. vol. 44 (1938) pp. 243-288.
- Robert Schmidt, Über divergente Folgen und lineare Mittelbildungen, Math. Z. 22 (1925), no. 1, 89–152 (German). MR 1544717, DOI 10.1007/BF01479600 A. Zygmund, Trigonometrical series, Warsaw-Lwów, 1935 331 pp.
Additional Information
- © Copyright 1948 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 63 (1948), 226-234
- MSC: Primary 40.0X
- DOI: https://doi.org/10.1090/S0002-9947-1948-0023932-9
- MathSciNet review: 0023932