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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2015, Number 4, Pages 55–57
(Mi vmumm254)
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Short notes
On a class of oscillating integrals
M. Sh. Shikhsadilov Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
The following result is proved in the paper: if for some real $A>0$ and some natural number $n>1$
for all $x$ from $[0,1]$ we have the inequality $|f^{(n)}(x)|\geq A,$ then the following estimate is valid:
$$
|I|=\left|\int_0^1\limits\rho(f(x))~dx\right|\leq\min{\{1;4nA^{-1/n}\}},
$$
where $\rho(t)=0,5-\{t\}.$
Key words:
“saw-tooth” function, trigonometric integrals.
Received: 28.11.2014
Citation:
M. Sh. Shikhsadilov, “On a class of oscillating integrals”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2015, no. 4, 55–57; Moscow University Mathematics Bulletin, 70:4 (2015), 191–192
Linking options:
https://www.mathnet.ru/eng/vmumm254 https://www.mathnet.ru/eng/vmumm/y2015/i4/p55
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