Recovering fourier coefficients of some functions and factorization of integer numbers
Sergei Nikolaevich Preobrazhenskii · Moscow University Mathematics Bulletin · 2010
It is shown that if a function determined on the segment [−1, 1] has a sufficiently good approximation by partial sums of its expansion over Legendre polynomial, then, given the function’s Fourier coefficients c n for some subset of n ∈ [n 1, n 2], one can approximately recover them for all n ∈ [n 1, n 2]. A new approach to factorization of integer numbers is given as an application.