摘要
As a typical family of mono-component signals,the nonlinear Fourier basis {eikθa(t)}k∈Z,defined by the nontangential boundary value of the M¨obius transformation,has attracted much attention in the field of nonlinear and nonstationary signal processing in recent years.In this paper,we establish the Jackson's and Bernstein's theorems for the approximation of functions in Xp(T),1 p ∞,by the nonlinear Fourier basis.Furthermore,the analogous theorems for the approximation of functions in Hardy spaces by the finite Blaschke products are established.
As a typical family of mono-component signals,the nonlinear Fourier basis {eikθa（t）}k∈Z,defined by the nontangential boundary value of the M¨obius transformation,has attracted much attention in the field of nonlinear and nonstationary signal processing in recent years.In this paper,we establish the Jackson＇s and Bernstein＇s theorems for the approximation of functions in Xp（T）,1 p ∞,by the nonlinear Fourier basis.Furthermore,the analogous theorems for the approximation of functions in Hardy spaces by the finite Blaschke products are established.
基金
supported by National Natural Science Foundation of China (Grant Nos.11071261,60873088,10911120394)
