Invariant subspaces in certain function spaces on the simplest solvable lie group

INVARIANT SUBSPACES IN CERTAIN FUNCTION SPACES ONn-DIMENSIONAL LOBACHEVSKY SPACE

“…The first step in the solution of this problem was made in [2]. An analogous problem can be posed for symmetric spaces of rank 1.…”

“…This problem was solved in [2]. We present the results needed for what follows (with some corrections).…”

“…See [2] (p. 198, Proposition 1.1) for a proof. The set Ρ(λ, μ) of operators can be described in a more explicit form.…”

“…See [2] (p. 201, Corollary 1.2) for a proof. Denote the set of elements in Ρ(λ,μ) of the form L(pi,...,p n ;a\,...,a n )…”

“…See [2] for a proof of Proposition 3.2 (p. 201, the proof of Proposition 1.2). We note only that the formulation of Proposition 1.2 in [2] is valid only for an irreducible Ε (it coincides with the formulation of Corollary 3.1), but the proof works in the general case.…”