Abstract:A subspace $W$ of the Schwartz space $C^{\infty} (a,b)$ such that the restriction of the operator of differentiation to $W$ has a discrete spectrum is considered. Conditions for the representation of $W$ as a direct algebraic and topological sum of two subspaces, namely, the residual subspace and the subspace spanned by the exponential monomials from $W$, are investigated. One condition ensuring this representation turns out to be the existence of a functional annihilating $W$ such that the Fourier-Laplace tra… Show more
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