On spectral properties of $p$-adic pseudodifferential operators of Schrödinger type

Spectral problems are considered for $p$-adic pseudodifferential operators of Schrödinger type for open-closed sets (bounded or not) in the space $Q_p^n$ with a potential tending to $+\infty$ at infinity. Some inversion theorems are proved. A method is presented and justified for constructing all eigenfunctions and eigenvalues for $M$-invariant symbols.