Tauberian theorems and slowly varying functions

Tauberian theorems and slowly varying functions
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by David Drasin

Trans. Amer. Math. Soc. 133 (1968), 333-356

DOI: https://doi.org/10.1090/S0002-9947-1968-0226017-4

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References

Albert Edrei and Wolfgang H. J. Fuchs, The deficiencies of meromorphic functions of order less than one, Duke Math. J. 27 (1960), 233–249. MR 123717
Albert Edrei and W. H. J. Fuchs, Tauberian theorems for a class of meromorphic functions with negative zeros and positive poles, Contemporary Problems in Theory Anal. Functions (Internat. Conf., Erevan, 1965) Izdat. “Nauka”, Moscow, 1966, pp. 339–358. MR 0213561
William Feller, On the classical Tauberian theorems, Arch. Math. (Basel) 14 (1963), 317–322. MR 155131, DOI 10.1007/BF01234960
William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
G. H. Hardy and W. W. Rogosinski, Notes on Fourier series. III. Asymptotic formulae for the sums of certain trigonometrical series, Quart. J. Math. Oxford Ser. 16 (1945), 49–58. MR 14159, DOI 10.1093/qmath/os-16.1.49

Sur un mode de croissance régulière des fonctions

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J. Karamata, Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze, Math. Z. 33 (1931), no. 1, 294–299 (German). MR 1545213, DOI 10.1007/BF01174355

The theory of functions

G. Valiron, Sur les fonctions entières d’ordre nul et d’ordre fini et en particulier les fonctions à correspondance régulière, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. (3) 5 (1913), 117–257 (French). MR 1508338

The Laplace transform