一类等距结点上的双周期整插值问题

The 2-Periodic Entire Interpolation on Equidistant Nodes

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.

On nodal sets xk=（a〉0.k∈z）given positive integersm1〈m2〈m3and series of complexnumber {ak,i }k∈z satisfying∑^＋∞ k=-∞/ak,j/〈∞（j=0,1,2,3）an entire function{ak,j}k∈Zis found satisfying：T（x2k＋1）=ak0 T^（m1）（x2k）=ak1 T^（m2）（x2k）=ak2 T^（m3）（x2k）=ak3 By applying the property of basic interpolation polynomials, some equation sets which have the same de terminant of coefficient are established, and then using Cramer＇ rule, the sufficient condition of the solva bility of the interpolation is obtained. In the end, the explicit formulae of the interpolation function are de termined if it exists.