CAJ | 학술논문

证明了当f∈PWπ时,‖s(k)2mf-f(k)‖Lp(R)→0(m→∞,2≤p≤∞,k=0,1,2,…),其中PWπ是经典的Paley-Wiener类,s2mf是在实Riesz基序列上对f插值的唯一确定2m-1次缓增样条.同时还证明了当{f(tj)}∈l2,f∈Lp(R)(p≥2),‖s2mf‖2≤A一致成立时,若limm→∞‖f-s2mf‖p=0,则f∈Bπ,p,其中Bπ,p为指数π型整函数在R上的限制与Lp(R)的交.
증명료당f∈PWπ시,‖s(k)2mf-f(k)‖Lp(R)→0(m→∞,2≤p≤∞,k=0,1,2,…),기중PWπ시경전적Paley-Wiener류,s2mf시재실Riesz기서렬상대f삽치적유일학정2m-1차완증양조.동시환증명료당{f(tj)}∈l2,f∈Lp(R)(p≥2),‖s2mf‖2≤A일치성립시,약limm→∞‖f-s2mf‖p=0,칙f∈Bπ,p,기중Bπ,p위지수π형정함수재R상적한제여Lp(R)적교.
It is proved that if f∈PWπ, then ‖s(k)2mf-f(k)‖Lp(R)→0 asm→∞,2<p≤∞,k=1,2,…, where PWπ denotes the classical Paley-Wiener class, s2mf is the unique tempered spline of degree 2m-1 interpolating to f at real Riesz basis sequence.