用Hermite函数的积分逼近积分型函数
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摘要
讨论了用Hermite函数的积分去逼近积分型函数的问题,给出了投影P_Nw(x)的原函数是平方可积的充分必要条件,得到了误差的L~2(R)范数的上界.
We investigate the problem of approximating the integral function by the integral of Hermite functions. We give an equivalent condition for the primitive function of the projection P_Nw(x) to be square integrable. Moreover, we obtain an upper bound for the approximation error under the L~2(R) norm.
We investigate the problem of approximating the integral function by the integral of Hermite functions. We give an equivalent condition for the primitive function of the projection P_Nw(x) to be square integrable. Moreover, we obtain an upper bound for the approximation error under the L~2(R) norm.
引文
[1] 孙美芳,吴嘎日迪.Orlicz空间内两类插值逼近的Stechkin-Marchaud不等式[J].大学数学,2018,34(1):1-6.
[2] Xiang X M,Wang Z Q.Generalized Hermite spectral method and its applications to problems in unbounded domains[J].SIAM J.Numer.Anal.,2010,48(4):1231-1253.
[3] Gan Z H,Guo B L,Zhang J.Instability of standing wave,global existence and blowup for the Klein-Gordon-Zakharov system with different-degree nonlinearities[J].J.Differential Equations,2009,246(10):4097-4128.
[4] Tang T.The Hermite spectral method for Gauss-type function[J].SIAM J.Sci.Comput.,1993,14(3):594-606.
[5] Szeg? G.Orthogonal polynomials,revised ed.[M].Providence,RI:Amer.Math.Soc.Colloq.Pub.23,AMS,1959:104-105.
[6] 谌德.Hermite函数的原函数的平方可积性[J].大学数学,2017,33(6):63-65.
[7] 王明新.索伯列夫空间[M].北京:高等教育出版社,2013:145-146.
[2] Xiang X M,Wang Z Q.Generalized Hermite spectral method and its applications to problems in unbounded domains[J].SIAM J.Numer.Anal.,2010,48(4):1231-1253.
[3] Gan Z H,Guo B L,Zhang J.Instability of standing wave,global existence and blowup for the Klein-Gordon-Zakharov system with different-degree nonlinearities[J].J.Differential Equations,2009,246(10):4097-4128.
[4] Tang T.The Hermite spectral method for Gauss-type function[J].SIAM J.Sci.Comput.,1993,14(3):594-606.
[5] Szeg? G.Orthogonal polynomials,revised ed.[M].Providence,RI:Amer.Math.Soc.Colloq.Pub.23,AMS,1959:104-105.
[6] 谌德.Hermite函数的原函数的平方可积性[J].大学数学,2017,33(6):63-65.
[7] 王明新.索伯列夫空间[M].北京:高等教育出版社,2013:145-146.