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- W2083641178 abstract "Let $F:Xrightarrow X$ be a $C^k(X)$, $k=[0, infty]$, map on a topological space (smooth manifold) $X$, $A:Xrightarrow End(C^m)$ and let ${U_alpha}$ be an $Fmbox{-invariant}$ covering of $X$. We introduce spaces of cohomologies associated with ${U_alpha}$ and an operator $T=I - R$, where $(Rphi)(x)=A(x)phi(F(x))$ is a weighted substitution operator in $C^k(X)$. This yields a correspondence between $Im T$ and $Im T|U_alpha$ and the description of $Im T$ in cohomological terms. In particular, it is proven that for any structurally stable diffeomorphism on a circle and for large enough $k$, the operator $T$ is semi-Fredholm, and a similar result holds for the substitution operators generated by simple multidimensional maps. On the other hand, we show that, in general, the closures of $Im T$ and $Im T|U_alpha$ are independent." @default.
- W2083641178 created "2016-06-24" @default.
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- W2083641178 date "1998-04-01" @default.
- W2083641178 modified "2023-09-27" @default.
- W2083641178 title "Spaces of cohomologies associated with linear functional equations" @default.
- W2083641178 doi "https://doi.org/10.1017/s014338579810041x" @default.
- W2083641178 hasPublicationYear "1998" @default.
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