×

On weighted positivity of ordinary differential operators. (English) Zbl 0957.34078

Summary: “Some elliptic differential operators possess a weighted positivity property, where the weight is a fundamental solution to the operator. This property has interesting applications to partial differential operators. The present paper is devoted to the property for ordinary differential operators.
It is shown that the operator \((1-d^2/ dx^2)^m\) has the positivity property if and only if \(m=0,1,2,3\), while there exist operators of arbitrary even order for which the positivity holds. Some necessary conditions for the property are given”.

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
47E05 General theory of ordinary differential operators
34G20 Nonlinear differential equations in abstract spaces
PDFBibTeX XMLCite
Full Text: DOI EuDML