Continuous Linear Endomorphisms and Difference Equations over the Completion of Fq[T]

✍ Scribed by Sangtae Jeong

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 154 KB
• Volume: 84
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2000.2532

✦ Synopsis

We characterize continuous linear endomorphisms which commute with a fixed Carlitz difference operator on the space of continuous F q -linear functions defined over the completion of F q [T] in terms of a bounded sequence, which is closely related to hyper-differential operators. This leads us to establish that such an endomorphism has a unique expansion with respect to the Carlitz difference operators and then the solution space of difference equations is explicitly described.

2000 Academic Press

Recall that Q is a K-linear endomorphism of E if Q( f +g)=Q( f )+Q( g), Q(:f )=:Q( f ) for f, g # E and : # K. Throughout the paper, the focus will be on continuous linear endomorphisms of E commuting with 2 :=2 (1) , which we will denote by End K (E; 2).