Decomposition as the sum of invariant functions with respect to commuting transformations
| dc.creator | Farkas, Balint | |
| dc.creator | Revesz, Szilard | |
| dc.date | 2005-07-29 | |
| dc.date | 2007-03-12 | |
| dc.date.accessioned | 2026-07-07T07:51:08Z | |
| dc.date.available | 2026-07-07T07:51:08Z | |
| dc.description | Let A be an arbitrary set. For any transformation T (self-map of A) let T(f)(x):=f(T(x)) (for all x in A) be the usual shift operator. A function g is called periodic, i.e., invariant mod T, if Tg=g (=Ig, where I is the identity operator). As a natural generalization of various earlier investigations in different function spaces, we study the following problem. Let T_j (j=1,...,n) be arbitrary commuting mappings -- transformations -- from A into A. Under what conditions can we state that a function f from A to A is the sum of "periodic", that is, T_j-invariant functions f_j? An obvious necessary condition is that the corresponding multiple difference operator annihilates f, i.e., D_1 ... D_n f= 0, where D_j:=T_j-I. However, in general this condition is not sufficient, and our goal is to complement this basic condition with others, so that the set of conditions will be both necessary and sufficient. | |
| dc.identifier | https://arxiv.org/abs/math/0507605 | |
| dc.identifier | http://arxiv.org/abs/math/0507605 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125405 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 39A10 (Primary); 39B52, 39B72 (Secondary) | |
| dc.title | Decomposition as the sum of invariant functions with respect to commuting transformations | |
| dc.type | text |