On the convergence of biorthogonal series related to odd-order differential operators with nonsmooth coefficients
Let \({\mathcal L}\) be a differential operator generated by \[ \ell u \equiv u^{(n)}(x) +\sum_{k=0}^{n-1} a_k(x) u^{(k)}(x),\quad x\in G=(0,1), \] which acts on the class \(D_n\) of functions which are absolutely continuous on \([0,1]\) together with their derivatives up to order \(n-1.\) Here, \(a_{n-1}\in L^s(G)\) with \(s\geq1,\) \(a_k(x)\in L(G)\) for \(k=0,1,\dots,n-2\), where \(n=2l+1\) for some non-negative integer \(l.\) The authors estimate the rate of equiconvergence of spectral decompositions in root functions of the operator \({\mathcal L}.\)
scientific article; zbMATH DE number 5816897