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ON THE GROWTH RATE OF SLOWLY VARYING FUNCTIONS

$icon-email$ ALLAN GUT

Abstract

A function $L$ is slowly varying (at infinity) iff $\frac{L (t x)}{L (x)} \to 1$ as $x \to \infty$ for every $t > 0$ . Motivated by two examples we investigate to what extent, if at all, the limit of the ratio equals 1 when $t$ is replaced by some function of $x$ growing to infinity.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Mã bưu điện: 10072

Viện Hàn lâm Khoa học và Công nghệ Việt Nam Hội Toán học Việt Nam Viện Nghiên cứu Cao cấp về toán

Acta Mathematica Vietnamica

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ON THE GROWTH RATE OF SLOWLY VARYING FUNCTIONS

Abstract