Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 33-39
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S. N. Preobrazhenskii. Recovering fourier coefficients of some functions and factorization of integer numbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 33-39. http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/
@article{VMUMM_2010_4_a5,
author = {S. N. Preobrazhenskii},
title = {Recovering fourier coefficients of some functions and factorization of integer numbers},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {33--39},
year = {2010},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/}
}
TY - JOUR
AU - S. N. Preobrazhenskii
TI - Recovering fourier coefficients of some functions and factorization of integer numbers
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 2010
SP - 33
EP - 39
IS - 4
UR - http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/
LA - ru
ID - VMUMM_2010_4_a5
ER -
%0 Journal Article
%A S. N. Preobrazhenskii
%T Recovering fourier coefficients of some functions and factorization of integer numbers
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2010
%P 33-39
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a5/
%G ru
%F VMUMM_2010_4_a5
It is shown that if a function defined on the segment $[-1,1]$ has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function's Fourier coefficients $c_n$ for some subset of $n\in[n_1,n_2]$, one can approximately recover them for all $n\in[n_1,n_2]$. As an application, a new approach to factoring of integers is given.
