Convex regular domains of tridiagonal matrices

Abstract

This paper is concerned with tridiagonal matrices as functions of their diagonal vectors. Best possible convex domains of regularity are found for these matrices. Means of constructing such domains are also derived. These are then used to derive best possible conditions for the existence and uniqueness of solutions of boundary value problems involving difference equations. The idea behind this paper is based on observations of a simple two by two matrix, so that all the results obtained are original and self-contained.