We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or,...We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.展开更多
文摘We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.
