Problem of the theory of functions and essential self-adjointness of powers of operators
type: Item
instance of: scholarly article
title: Problem of the theory of functions and essential self-adjointness of powers of operators
zbMATH Open document ID: 0734.47015
DOI: 10.1007/BF01066189
author: Yu. B. Orochko
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 4214761
zbMATH Keywords: Essential selfadjointness
zbMATH Keywords: powers of a minimal symmetric operator generated by an elliptic differential expression of m variables
zbMATH Keywords: selfadjointness of the minimal Schrödinger operator
reviewed by: Teresa Regińska
MaRDI profile type: Publication
cites work: Q3291737
cites work: Q5540712
cites work: Q3262907
cites work: Essential self-adjointness of powers of generators of hyperbolic equations
cites work: Q5624013
cites work: Q3278549
cites work: A remark to the preceding paper by Chernoff
description: scientific article; zbMATH DE number 4214761