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On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-01
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper studies Volterra integral evolution equations of convolution type from the point of view of complex inversion formula and the admissibility in the Salamon-Weiss sens.
We first present results on the validity of the inverse formula of the Laplace transform for the resolvent families associated with scalar Volterra integral equations of convolution type in Banach spaces, which extends and improves the results in Hille and Philllips (1957) and Cioranescu and Lizama (2003, Lemma 5), respectively, including the stronger version for a class of scalar Volterra integrodifferential equations of convolution type on unconditional martingale differences UMD spaces, provided that the leading operator generates a C0-semigroup.
Next, a necessary and sufficient condition for Lp-admissibility p∈1,∞ of the system's control operator is given in terms of the UMD-property of its underlying control space for a wider class of Volterra integrodifferential equations when the leading operator is not necessarily a generator, which provides a generalization of a result known to hold for the standard Cauchy problem (Bounit et al., 2010, Proposition 3.2).
American Psychological Association (APA)
Fadili, Ahmed& Bounit, Hamid. 2014. On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems. International Journal of Differential Equations،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-510585
Modern Language Association (MLA)
Fadili, Ahmed& Bounit, Hamid. On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems. International Journal of Differential Equations No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-510585
American Medical Association (AMA)
Fadili, Ahmed& Bounit, Hamid. On the Complex Inversion Formula and Admissibility for a Class of Volterra Systems. International Journal of Differential Equations. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-510585
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-510585