As everyone knows,the classical Jackson theorem in approximation theory was generalized in Lp spaces by R.A.Devore.In this paper,we proved the Jackson theorem in B,spaces which introduced by Ding Xia Xi,
We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-function...We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.展开更多
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 non...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.展开更多
文摘As everyone knows,the classical Jackson theorem in approximation theory was generalized in Lp spaces by R.A.Devore.In this paper,we proved the Jackson theorem in B,spaces which introduced by Ding Xia Xi,
文摘We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.
基金supported by National Natural Science Foundation of China (Grant Nos.11071261,60873088,10911120394)
文摘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.
