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On the Spectrum of almost periodic solutions of an abstract differential equation

Published online by Cambridge University Press:  09 April 2009

Aribindi Satyanarayan Rao  and
Walter Hengartner
Aribindi Satyanarayan Rao
Affiliation:
Department of MathematicsUniversité Laval, Québec City, P. QuébecCanada.
Walter Hengartner
Affiliation:
Department of MathematicsUniversité Laval, Québec City, P. QuébecCanada.
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Abstract

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If a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 385 - 387
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Amerio, L. and Prouse, G., Almost periodic functions and functional equations, (Van Nostrand Reinhold Company (1971)).Google Scholar
[2]Dunford, V. and Schwartz, J. T., Linear operators, part I, (Interscience Publishers, Inc., New York (1958)).Google Scholar
[3]Zaidman, S., ‘An existence result for Stepanoff almost periodic differential equation’, Canad. Math. Bull. 14 (1971), 551–554.Google Scholar