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Criteria in Nuclear Fréchet Spaces and Silva Spaces with Refinement of the Cannon-Whittaker Theory
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-07
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Along with the theory of bases in function spaces, the existence of a basis is not always guaranteed.
The class of power series spaces contains many classical function spaces, and it is of interest to look for a criterion for this class to ensure the existence of bases which can be expressed in an easier form than in the classical case given by Cannon or even by Newns.
In this article, a functional analytical method is provided to determine a criterion for basis transforms in nuclear Fréchet spaces ((NF)-spaces), which is indeed a refinement and a generalization of those given in this concern through the theory of Whittaker on polynomial bases.
The provided results are supported by illustrative examples.
Then, we give the necessary and sufficient conditions for the existence of bases in Silva spaces.
Moreover, a nuclearity criterion is given for Silva spaces with bases.
Subsequently, we show that the presented results refine and generalize the fundamental theory of Cannon-Whittaker on the effectiveness property in the sense of infinite matrices.
American Psychological Association (APA)
Abul-Ez, Mahmoud& Zayed, Mohra. 2020. Criteria in Nuclear Fréchet Spaces and Silva Spaces with Refinement of the Cannon-Whittaker Theory. Journal of Function Spaces،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1185941
Modern Language Association (MLA)
Abul-Ez, Mahmoud& Zayed, Mohra. Criteria in Nuclear Fréchet Spaces and Silva Spaces with Refinement of the Cannon-Whittaker Theory. Journal of Function Spaces No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1185941
American Medical Association (AMA)
Abul-Ez, Mahmoud& Zayed, Mohra. Criteria in Nuclear Fréchet Spaces and Silva Spaces with Refinement of the Cannon-Whittaker Theory. Journal of Function Spaces. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1185941
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1185941