For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )...For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.展开更多
This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes...This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.展开更多
文摘For linear partial differential equation 〔 2t 2-a 2P( x)〕 m u=f(x,t), where m1,X∈R n,t∈R 1, the author gives the analytic solution of the initial value problem using the operators sh(tP( x) 1/2 )P( x) 1/2 . By representing the operators with integrals, explicit solutions are obtained with an integral form of a given function.
文摘This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.
