The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications
Joint Authors
Gilliam, D. S.
Ji, X.
Hohage, T.
Ruymgaart, Frits
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-04-14
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
The main result in this paper is the determination of the Fréchet derivative of an analytic function of a bounded operator, tangentially to the space of all bounded operators.
Some applied problems from statistics and numerical analysis are included as a motivation for this study.
The perturbation operator (increment) is not of any special form and is not supposed to commute with the operator at which the derivative is evaluated.
This generality is important for the applications.
In the Hermitian case, moreover, some results on perturbation of an isolated eigenvalue, its eigenprojection, and its eigenvector if the eigenvalue is simple, are also included.
Although these results are known in principle, they are not in general formulated in terms of arbitrary perturbations as required for the applications.
Moreover, these results are presented as corollaries to the main theorem, so that this paper also provides a short, essentially self-contained review of these aspects of perturbation theory.
American Psychological Association (APA)
Gilliam, D. S.& Hohage, T.& Ji, X.& Ruymgaart, Frits. 2009. The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-17.
https://search.emarefa.net/detail/BIM-456405
Modern Language Association (MLA)
Gilliam, D. S.…[et al.]. The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-17.
https://search.emarefa.net/detail/BIM-456405
American Medical Association (AMA)
Gilliam, D. S.& Hohage, T.& Ji, X.& Ruymgaart, Frits. The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-17.
https://search.emarefa.net/detail/BIM-456405
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-456405