On the Bounded Solutions of Volterra Equations
- 1 May 2004
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 83 (5) , 433-446
- https://doi.org/10.1080/00036810310001632781
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.Keywords
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