Equiconvergence. A generalization of the Tamarkin-Stone theorem (Q1277507)

Linear differential (nonselfadjoint) operators of arbitrary even order \( n \) are investigated. Every function from the domain of the operator satisfy \( n \) linearly independent normalized boundary conditions. The expansion of a function \( f \) in the root functions of the differential operator is investigated. The author establishes the equiconvergence of the expansion for operators of any even order and for an arbitrary given function \( f \in C [0,1] \) satisfying certain boundary conditions of zero order, i.e. those conditions that do not contain derivatives.