In the present article, approximation of function |sin x| s by partial sums rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for above-mentioned were obtained. Based on them, several special cases selection poles studied. case polynomial series, an asymptotic equality was found. A detailed study made a fixed number geometrically differ...

X iv :1 00 8. 50 35 v1 [ m at h. N T ] 3 0 A ug 2 01 0 RECOVERING FOURIER COEFFICIENTS OF MODULAR FORMS AND FACTORING OF INTEGERS Sergei N. Preobrazhenskĭi 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 cn for some subset of n ∈ [n1, n2], one c...

We establish asymptotic estimates for the least upper bounds of approximations in uniform metric by Fourier sums order n − 1 classes 2

In this paper, we derive a new recovery procedure for the reconstruction of extended exponential sums form [Formula: see text], where frequency parameters text] are pairwise distinct. order to reconstruct y(t) employ finite set classical Fourier coefficients y with regard interval text]. For our method, 2N + 2 sufficient recover all y, denotes y(t). The is based on observation that terms posses...

Approximation by trigonometric Fourier series is a well-developed branch of the theory approximation polynomials. Methods rational have not been researched so deeply yet. In particular, operators Fejér type used in with free poles. this paper, we consider function | sin , (0;2), ∈ s x type. An integral representation remainder for above-mentioned obtained. estimate approximations found points a...