Nontrivial expansions of zero absolutely representing systems (Q1907438)

The author introduces a method for constructing a sequence \(\{e(\lambda_k)\}_{k=1}^\infty\) in a Fréchet space \(F\) (where for each \(\lambda\in\mathbb{C}\) the vector \(e(\lambda)\) spans a one-dimensional subspace of solutions to an operator equation \(My= \lambda y)\) with the property that every element in \(F\) has an absolutely convergent expansion of the form \(\sum_{k=1}^\infty c_k e(\lambda k)\).