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On a representation of continuous Volterra right inverses to the derivative in the spaces of infinitely differentiable functions

Part of: General theory of linear operators Volterra integral equations

Published online by Cambridge University Press:  09 April 2009

Danuta Przeworska-Rolewicz  and
Stefan Rolewicz
Danuta Przeworska-Rolewicz
Affiliation:
Institute of Mathematics, of the Polish Academy of Sciences, Śniadeckich 8, 00 950 Warszawa, Poland
Stefan Rolewicz
Affiliation:
Institute of Mathematics, of the Polish Academy of Sciences, Śniadeckich 8, 00 950 Warszawa, Poland
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Abstract

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Every continuous Volterra right inverse to the derivative in the space of complex-valued infinitely differentiable functions has the form of an integral.

Keywords

Volterra operatorsright invertible operators

MSC classification

Secondary: 47A67: Representation theory 45D05: Volterra integral equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 138 - 142
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Przeworska-Rolewicz, D. and Rolewicz, S., ‘The only continuous right inverse in Cc[0,1] of the operator d/dt are ∫ta’, Colloq. Math., to appear.Google Scholar
[2]Przeworska-Rolewicz, D., ‘Shifts and periodicity for right invertible operators’, (Research Notes in Mathematics 43, Pitman Adv. Publish. Program, London, Boston, Melbourne, 1980).Google Scholar
[3]Przeworska-Rolewicz, D., ‘Admissible initial operators for superpositions of right invertible operators’, Ann. Polon. Math. 33 (1977), 312–318.Google Scholar
[4]Rolewicz, S., Metric linear spaces, (2nd ed., Reidel, D.Publishing Co. and PWN, Dordrecht, Warszawa, 1985).Google Scholar
[5]Saks, S. and Zygmund, A., Analytic functions (Monograf. Mat. 28, 2nd ed., PWN, Warszawa, Wrocaw, 1965).Google Scholar