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A note on invariant subspaces and the solution of some classical functional equations | | J. M. Almira
; Kh. F. Abu-Helaiel
; | | Date: |
29 Oct 2013 | | Abstract: | We study the continuous solutions of several classical functional equations
by using the properties of the spaces of continuous functions which are
invariant under some elementary linear trans-formations. Concretely, we use
that the sets of continuous solutions of certain equations are closed vector
subspaces of $C(mathbb{C}^d,mathbb{C})$ which are invariant under affine
transformations $T_{a,b}(f)(z)=f(az+b)$, or closed vector subspaces of
$C(mathbb{R}^d,mathbb{R})$ which are translation and dilation invariant.
These spaces have been recently classified by Sternfeld and Weit, and Pinkus,
respectively, so that we use this information to give a direct characterization
of the continuous solutions of the corresponding functional equations. | | Source: | arXiv, 1310.7844 | | Services: | Forum | Review | PDF | Favorites | |
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