Abstract
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.
Highlights
Introduction and motivationThe wide area of ordinary differential equations and various types of ordinary difference equations is always closely connected to special function systems
The intention of this article is to address specific problems which are related to so-called basic adaptive discretizations: Starting from conventional difference and differential equations, we move on to basic difference equations
There, we look in greater detail at solutions of underlying moment problems
Summary
Introduction and motivationThe wide area of ordinary differential equations and various types of ordinary difference equations is always closely connected to special function systems. Where Pj is a fixed function of an orthogonal polynomial system P, z , and z being adjacent nodes of Pj. For a fixed value j ∈ N , we start from the defining equation aj+ Pj+ (x) – xbj+ Pj+ (x) + cjPj(x) = djPj+ (x). The following statements hold: ( ) The evaluation of all elements Pm (m ∈ N ) of the tripolynomial function system at two adjacent nodes z and z of the particular polynomial Pj yields complete information on a sequence of new polynomials Tn (n ∈ N ).
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