On the similarity of some differential operators to self-adjoint ones
type: Item
instance of: scholarly article
title: On the similarity of some differential operators to self-adjoint ones
zbMATH Open document ID: 1048.47031
DOI: 10.1023/A:1019810314450
author: M. M. Faddeev
author: Roman Shterenberg
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The paper under review deals with the problem of the similarity of differential operators of the form \[ L= (-\text{sign\,}x/| x|^\alpha p(x)) d^2/dx^2 \] (where \(\alpha> -1\) and \(0< c< p(x)< C<+\infty\)) to selfadjoint ones. The operator \(L\) is defined in the space of square integrable functions on the axis with the weight \(p(x)| x|^\alpha\) on the domain \(D(L)\) consisting of functions \(f\in L^2(p(x)| x|^\alpha, \mathbb{R})\) being absolutely continuous together with their first derivatives and such that \(Lf\in L^2(p(x)| x|^\alpha,\mathbb{R})\).
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1928284
zbMATH Keywords: similarity problem
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: a:1019810314450
OpenAlex ID: W185926576
description: scientific article; zbMATH DE number 1928284