The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use o...The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.展开更多
The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle ...The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).展开更多
文摘The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.
基金supported by the Innovation Research for the Postgrad-uates of Guangzhou University(2020GDJC-D06)supported by the National Natural Science Foundation of China(12071229)。
文摘The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).
