Geodesic
On a class of oscillating integrals
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 55-57

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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 $\rho(t)=0,5-\{t\}.$ 
@article{VMUMM_2015_4_a9,
     author = {M. Sh. Shikhsadilov},
     title = {On a class of oscillating integrals},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {55--57},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a9/}
}
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M. Sh. Shikhsadilov. On a class of oscillating integrals. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 55-57. http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a9/