In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obta...In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.展开更多
We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating v...We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating varieties.展开更多
给定结点组xk=kπ/σ(σ>0,k∈Z),对于正整数m1<m2<m3及满足条件(sum from k=-8 to +∞)︱αk,j︱<∞(j=0,1,2,3)的复数序列{αk,j}k∈Z,寻找整函数T∈B22σ,使其满足插值条件:T(x2k+1)=αk0 T(m1)(x2k)=αk1T(m2)(x2k)=αk...给定结点组xk=kπ/σ(σ>0,k∈Z),对于正整数m1<m2<m3及满足条件(sum from k=-8 to +∞)︱αk,j︱<∞(j=0,1,2,3)的复数序列{αk,j}k∈Z,寻找整函数T∈B22σ,使其满足插值条件:T(x2k+1)=αk0 T(m1)(x2k)=αk1T(m2)(x2k)=αk2 T(m3)(x2k)=αk3利用插值基多项式的性质建立了具有相同系数行列式的方程组,之后运用克拉默法则给出了整插值问题解存在的充分条件,同时给出相应条件下解的显式.展开更多
文摘In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.
文摘We discuss some recent results on interpolation problems for weighted Hrmander’s algebras of holomorphic functions in several complex variables, and also give a sharp estimate on counting functions of interpolating varieties.
文摘给定结点组xk=kπ/σ(σ>0,k∈Z),对于正整数m1<m2<m3及满足条件(sum from k=-8 to +∞)︱αk,j︱<∞(j=0,1,2,3)的复数序列{αk,j}k∈Z,寻找整函数T∈B22σ,使其满足插值条件:T(x2k+1)=αk0 T(m1)(x2k)=αk1T(m2)(x2k)=αk2 T(m3)(x2k)=αk3利用插值基多项式的性质建立了具有相同系数行列式的方程组,之后运用克拉默法则给出了整插值问题解存在的充分条件,同时给出相应条件下解的显式.
