Abstract:
The spectrum of the internal superposition operator, defined as a linear combination of shift operators acting in Lebesgue spaces of functions on a semiaxis, is studied. For cases where the shifts are commensurate or linearly independent over a set of integers, an effective description of the spectrum is found in terms of the parameters of the original operator. The results obtained are applied to the study of the solvability and stability of functional and functional differential equations.
|
