Geodesic
A Tauberian Theorem of Exponential Type
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 697-718

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. We will be interested in Tauberian theorems concerning the limiting behaviour of a monotone function U and its Laplace transform A famous theorem of Karamata concerns the case in which the function U is regularly varying (i.e., U(tx)/U(t) → xα (t → ∞) for x > 0). Here we will consider functions U that grow faster, in fact our conditions will be in terms of log U rather than on U itself. So it is convenient to write the Laplace transform in terms of q = log U. For a function q:R + → R such that exp q is locally integrable and we define the function by the relation 
Geluk, J. L.; Haan, L. de; Stadtmüller, U. A Tauberian Theorem of Exponential Type. Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 697-718. doi: 10.4153/CJM-1986-036-x
@article{10_4153_CJM_1986_036_x,
     author = {Geluk, J. L. and Haan, L. de and Stadtm\"uller, U.},
     title = {A {Tauberian} {Theorem} of {Exponential} {Type}},
     journal = {Canadian journal of mathematics},
     pages = {697--718},
     year = {1986},
     volume = {38},
     number = {3},
     doi = {10.4153/CJM-1986-036-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-036-x/}
}
TY  - JOUR
AU  - Geluk, J. L.
AU  - Haan, L. de
AU  - Stadtmüller, U.
TI  - A Tauberian Theorem of Exponential Type
JO  - Canadian journal of mathematics
PY  - 1986
SP  - 697
EP  - 718
VL  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-036-x/
DO  - 10.4153/CJM-1986-036-x
ID  - 10_4153_CJM_1986_036_x
ER  - 
%0 Journal Article
%A Geluk, J. L.
%A Haan, L. de
%A Stadtmüller, U.
%T A Tauberian Theorem of Exponential Type
%J Canadian journal of mathematics
%D 1986
%P 697-718
%V 38
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-036-x/
%R 10.4153/CJM-1986-036-x
%F 10_4153_CJM_1986_036_x

[1] 1. Aljancić, S. and Arandelović, D., 0-regularly varying functions, Publ. de l'Inst. Math. Beograd 22 (1977), 5–22. Google Scholar

[2] 2. Balkema, A. A., Geluk, J. L. and de Haan, L., An extension of Karamatas Tauberian theorem and its connection with complementary convex functions, Quart. J. Math. Oxford (2) 30 (1979), 385–416. Google Scholar

[3] 3. Balkema, A. A. and Haan, L. de, On R. von Mises’ condition for the domain of attraction of exp(–e–x), Ann. Math. Stat. 43 (1972), 1352–1354. Google Scholar

[4] 4. Geluk, J. L., On regular variation and its applications in number theory, Ph. D. thesis, University of Leiden (1983). Google Scholar

[5] 5. Haan, L. de, On regular variation and its application to the weak convergence of sample extremes, Math. Centre Tracts 32 (Amsterdam, 1970). Google Scholar

[6] 6. Haan, L. de and Resnick, S. I., Stochastic processes and point processes, Report 8136/S, Econometric Inst., Erasmus University (1981). Google Scholar

[7] 7. Haan, L. de and Resnick, S. I., Asymptotically balanced functions and stochastic compactness of sample extremes, Ann. Prob. (1984), to appear. Google Scholar | DOI

[8] 8. Haan, L. de and Stadtmüller, U., Dominated variation and related concepts and Tauberian theorems for Laplace transforms, J. Math. Anal. Appl. 108 (1985), 344–365. Google Scholar

[9] 9. Kohlbecker, E. E., Weak asymptotic properties of partitions, Trans. Amer. Math. Soc. 88 (1958), 346–365. Google Scholar

[10] 10. Korevaar, J., Aardenne-Ehrenfest, T. van and de Bruijn, N. G., A note on slowly oscillating functions, Nw. Arch. Wisk. 23 (1949), 77–86. Google Scholar

[11] 11. Krasnosel'skii, M. A. and Rutickii, Ya. B., Convex functions and Orlicz spaces (Noordhoff, Groningen, 1961). Google Scholar

[12] 12. Wagner, E., Ein reeller Tauberscher Satzfur die Lap lace-Transformation, Math. Nachr. 36 (1968), 323–331. Google Scholar

Cité par Sources :