Weighted trigonometrical approximation onR1 with application to the Germ field of a stationary Gaussian noise

f∗(γ) (\(\gamma = a + ib\)) denotes the regular extension of \(f^{{\ast}}(a) = f(a)^{{\ast}}\) so that \(f^{{\ast}}(\gamma ) = (f(\gamma ^{{\ast}}))^{{\ast}}\), (\(\gamma ^{{\ast}} = a - ib\)).