A theorem on equiconvergence for differential operators of higher order with a singularity
The author considers nonselfconjugated boundary value problems \({\mathcal L}\) of the following form: \[ ly=\lambda y,\quad 0< x< T,\quad l\in V,\quad y(x)= O(x^{\mu_{m+1}}),\quad x\to 0, \] \[ V_j(y)\equiv y^{(\tau_j)}(T)+ \sum^{\tau_j- 1}_{k= 0} v_{jk} y^{(k)}(T)= 0,\quad j= 1,\dots, m,\quad 0\leq \tau_j\leq n-1,\quad \tau_j\neq\tau_s\quad (j\neq s). \] He obtains a theorem on the equiconvergence of the expansion of solutions into Fourier series with respect to eigen- and adjoint functions for the boundary value problems inside a finite interval \((0,T)\).
nonselfconjugated boundary value problems
scientific article; zbMATH DE number 1309952