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Dichotomic Behavior of Linear Difference Systems with Advanced Argument

✍ Scribed by Lolimar Dı́az; Raúl Naulin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
132 KB
Volume
248
Category
Article
ISSN
0022-247X

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✦ Synopsis

A n y n q B n y g n is considered. The sequence of advances g n satisfies Ž .

Ž . 1 F g n y n F N, where N is a fixed number. The matrices A n are invertible, Ž . whereas, in general, matrices B n are not. In this paper the notion of an ordinary dichotomy for a linear equation with advance is given. This construction relies on a Ž variation of constants formula obtained for the nonhomogeneous equation y n q . Ž . Ž . Ž . Ž Ž .. Ž . 1 s A n y n q B n y g n q f n and on the notion of admissibility of a pair of functional spaces. It is proven that these ordinary dichotomies are not destroyed by l 1 -perturbations. A theorem of existence of ordinary dichotomies is given.

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