Problem of the theory of functions and essential self-adjointness of powers of operators
A connection was established between the following facts: 1. Uniqueness of the set \(\{\rho (\lambda),a_ 0,...,a_{n-1}\}\) of a complex function \(\rho\) of bounded variation, continuous from the left, and complex numbers \(a_ i\), which is the solution of the equation \[ (1)\quad \int^{\infty}_{-\infty}\cos (\lambda^{\frac12}t)d\rho (\lambda)+\sum^{n-1}_{k=0}a_ k \cos (p_ k^{\frac12}t)=0\quad \forall t\in R; \] 2. Essential selfadjointness in \(L^ 2(R^ m)\) of powers of a minimal symmetric operator generated by an elliptic differential expression of m variables. The presented result is a generalization of \textit{B. M. Levitan}'s result [Usp. Math. Nauk 16, No. 4(100), 175-178 (1961; Zbl 0106.071)] concerning the uniqueness of the solution of (1) for \(a_ i=0\), \(i=0,...,n-1\) and the selfadjointness of the minimal Schrödinger operator.
powers of a minimal symmetric operator generated by an elliptic differential expression of m variables
selfadjointness of the minimal Schrödinger operator
scientific article; zbMATH DE number 4214761
scientific article