On the Bounded Solutions of Volterra Equations

Authors: Toshiki Naito, Nguyễn Văn Minh, James Liu,

https://doi.org/10.1080/00036810310001632781

Publisher, magazine: ,

Publication year: 2004

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Abstract

We extend the method of sums of commuting operators to the study of the existence and uniqueness of bounded solutions of Volterra equations of the form with bounded f in the infinite dimensional case. The main results are necessary and sufficient conditions for the above equations to have a unique bounded solution with spectrum not intersecting the spectrum of the equation under consideration. Applications are made to illustrate the main results.

Tags: Volterra equations, Sums of commuting operators, Spectrum of functions, Bounded solutions, Periodic solutions, Quasi-periodic solutions, Almost periodic solutions