Timeline for Differentiating an integral that grows like log asymptotically

9 events

when toggle format	what		by	license	comment
Jan 14, 2019 at 12:53	vote	accept	random_person
Jan 14, 2019 at 12:45	comment	added	Mateusz Kwaśnicki		@random_person: I just started to type when Iosif Pinelis gave esentially the same construction. I can oly add that what I meant in my first comment was Theorem 3.6.8 in the BGT book, which gives a necessary and sufficient condition for the desired asymptotics of $f$ in terms of its primitive function. See also Sections 3.7.1–3.7.2 therein.
Jan 14, 2019 at 12:19	comment	added	random_person		@MateuszKwaśnicki Thanks, I am looking forward to your answer.
Jan 14, 2019 at 10:48	comment	added	Mateusz Kwaśnicki		Original asymptotic equation is equivalent to $f$ being in the right de Haan class. Two-sided estimate would correspond to de Haan's analogue of $O$-regular variation, I think, and it does not follow automatically. The counter-example is less explicit, though, I will type it later today on a computer, if you like.
Jan 14, 2019 at 9:40	comment	added	random_person		What about bounds? Is it possible to show that there exists some $C > 0$ such that $\frac{1}{Ct} \le f(t) \le \frac{C}{t}$ for $t$ sufficiently large?
Jan 14, 2019 at 9:33	history	edited	Raziel	CC BY-SA 4.0	added 20 characters in body
Jan 14, 2019 at 9:23	history	edited	Raziel	CC BY-SA 4.0	added 15 characters in body
Jan 14, 2019 at 9:05	history	edited	Raziel	CC BY-SA 4.0	added 38 characters in body
Jan 14, 2019 at 9:00	history	answered	Raziel	CC BY-SA 4.0