Commutative ordinary differential operators

Abstract

The paper is conveniently divided into two sections. The first contains the general argument and the main propositions unencumbered by proof: in the first paragraph of this section is collected material already published; the succeeding paragraphs of the section are devoted to new results. The second section of the paper includes proofs of these results, together with certain corollaries not essential to the main argument. Part 1. I.—Preamble. We make certain notational conventions. There is a single independent variable x ; the arbitrary dependent variable of a differential equation or operation is written y . With these exceptions Greek letters denote functions of x and English “lower-case” letters denote constants.