By Prof. Kevin F. Clancey, Prof. Israel Gohberg
A few years aga the authors begun a undertaking of a publication at the concept of platforms of one-dimensional singular critical equa tions which was once deliberate as a continuation of the monograph by way of one of many authors and N. Ya. Krupnik ~~ bearing on scalar equa tions. This set of notes was once initiated as a bankruptcy facing difficulties of factorization of matrix capabilities vis-a-vis appli cations to structures of singular fundamental equations. operating systematically onthischapter and including alongside the best way new issues of view, new proofs and effects, we eventually observed that the cloth hooked up with factorizations is of self sustaining curiosity and we made up our minds to submit this bankruptcy as aseparate quantity. actually, due to fresh task, the volume of fabric was once really huge and we speedy realized that we won't disguise the entire leads to entire element. now we have attempted to incorporate a represen tative number of all types of equipment, techniques,results and functions. aside of the present paintings exposes effects from the Russian literature that have by no means seemed in English translation. we now have additionally determined to mirror a number of the contemporary effects which make attention-grabbing connections among factorization of matrix services and structures concept. the sphere is still very energetic and plenty of effects and connec tions are nonetheless now not weIl understood. those notes can be considered as a stepping stone to extra improvement. The authors desire that someday they are going to go back to accomplish their unique plan.