Remarks on the Wronskian and on sums decompositions

Abstract

We make a number of remarks on some theorems and considerations contained in the recent and valuable monograph [9]. The connection of the Wronskian with the linear dependence, the local linear dependence and the local linear independence is considered. The necessary and/or sufficient conditions in order that a function $ h(x,y) $ has the form $ \sum^n_{i=1} f_i(x)g_i(y) $ , in terms of the Wronski matrix, are discussed. The d'Alembert equation $ hh_{xy} - h_xh_y = 0 $ is investigated, too. We formulate also some open problems.