具有一个指标的离散函数空间的一般插值公式

本文对于由具有一个指标的离散函数组成的离散泛函空间建立了一系列内插公式。这些内插公式给出了离散模、最大模和Lipschitz商、H(?)lder商之间的关系,大量文献证明,这些内插公式及其推论在微分方程的有限差分逼近理论中是十分有用的。

General Interpolation Formulas for Spaces of Discrete Functions With One Index

The purpose of the present work is to establish a series of general interpolation formulas for the discrete functional spaces of discrete functions with one index in somewhat complete forms. These general interpolation formulas give the connected relationship among the discrete norms as the summations of powers, the maximum modulo and the Lipschitz and Holder quotients for different discrete functional spaces. Also a series of consequences, derivations and applications of these obtained interpolation formulas are justified which are useful for the further study in the finite difference approximations of the theory of partial differential equations.