Invariant subspaces in some function spaces on the light cone in~$\mathbb R^3$
Sbornik. Mathematics, Tome 203 (2012) no. 6, pp. 864-892
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For certain topological vector spaces of functions on the light cone $X$ in $\mathbb R^3$ we obtain a complete description of all the closed linear subspaces which are invariant with respect to the natural quasiregular representation of the group $\mathbb R\oplus\operatorname{SO}_0(1,2)$. In particular, we give a description of irreducible and indecomposable invariant subspaces. Among the function spaces we consider we include, in particular, the spaces $C(X)$ and $\mathscr E(X)$ of continuous and infinitely differentiable functions on $X$ and also function spaces formed by functions with exponential growth on $X$.
Bibliography: 32 titles.
Keywords:
invariant subspaces, quasiregular representation, light cone, homogeneous spaces, harmonic analysis.
@article{SM_2012_203_6_a4,
author = {S. S. Platonov},
title = {Invariant subspaces in some function spaces on the light cone in~$\mathbb R^3$},
journal = {Sbornik. Mathematics},
pages = {864--892},
publisher = {mathdoc},
volume = {203},
number = {6},
year = {2012},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2012_203_6_a4/}
}
S. S. Platonov. Invariant subspaces in some function spaces on the light cone in~$\mathbb R^3$. Sbornik. Mathematics, Tome 203 (2012) no. 6, pp. 864-892. http://geodesic.mathdoc.fr/item/SM_2012_203_6_a4/