Difference-differential operators for basic adaptive discretizations and their central function systems Oscillation of Difference, Differential, and Dynamic Equations

Abstract

The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail. © 2012 Birk et al.; licensee Springer.