Abstract:
Local versions of the Brown-Schreiber-Taylor theorem on spectral analysis in $\mathbb R^n$ are obtained under most general assumptions. This has made it possible, in particular, to prove the equivalence of the global and the local Pompeiu properties for a compact subset $E$ of $\mathbb R^n$ without any assumptions on $E$. Perfect analogues of these results are established for systems of convolution equations on the Heisenberg group $H^n_{\mathrm{red}}$. As an application, for subspaces of $C(H^n_{\mathrm{red}})$ invariant under shifts and unitary transformations a spectral synthesis theorem
is proved, analogues of which were known before only for functions of slow
growth.
Bibliography: 20 titles.
Fulltext:
PDF file (725 kB)
