Finite Fourier Coefficients is Best Approximation to f∈L_(p,α,β)

Hala Nama Kazem and Eman Samer Bhaya

Real or complex Fourier series are a very good methods to approximate function using only the first few terms (i.e. trancuting the sum to the term n ). This has good applications in the compression of music in players and the compression of digital image in JPEG form: By obtaing good approximation to the wave form of music and image in terms of Finite Fourier series. In this paper we introduce some approximation properties of the finite Fourier transform. We prove direct estimates in term of the weighted modulus of smoothness for functions in , - Also we introduce a version of Riemann-Lébesgue lemma for functions in the spaces that we defined.

Volume 12 | Issue 5

Pages: 193-199

DOI: 10.5373/JARDCS/V12I5/20201704