Geodesic
A new representation of slowly varying functions
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2001), pp. 47-52.

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For a slowly varying function $L(t)$ a new integral representation is obtained: $$L(t)=\eta(t)\int\limits_{t_0}^t b(x)d\ln x, t \geq t_0>0,$$ where $\eta(t)$ is measurable on $[t_0, +\infty), b(t)$ is continuous on $[t_0, + \infty)$ and $\lim\limits_{t \rightarrow + \infty} (b(t) / L(t))= 0$. This representation allows to generalize D.D. Adamovich’s classical result on equivalent slowly varying functions and to extend the statement of A. A. Goldberg theorem.
Keywords: slowly varying function, Goldberg theorem. 
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E. A. Danielyan; G. V. Mikaelyan. A new representation of slowly varying functions. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2001), pp. 47-52. http://geodesic.mathdoc.fr/item/UZERU_2001_1_a2/

[1] E. Seneta, Pravilno menyayuschiesya funktsii, Nauka, M., 1985 | MR | Zbl

[2] A. A. Goldberg, “Integralnoe predstavlenie monotonnykh medlenno menyayuschikhsya funktsii”, Izv. vuzov. Ser. matem., 1988, no. 4, 21–27 | MR | Zbl

[3] I. E. Danielyan, G. V. Mikaelyan, “Zamechaniya o predstavleniyakh medlenno menyayuschikhsya funktsii”, GIUL, Modelirovanie, optimizatsiya, upravlenie, 2000, no. 3, 57–64

[4] D. D. Adamovic, “Sur quelques proprie’te’s des fonctions a’ croissance lente de Karamata, I, II”, Matematicki Vesnik, 1966, no. 3, 161–172 | MR | Zbl