R.Hilscher

Spectral properties of general self-adjoint, even order differential operators

Abstract

Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator

l(y)=1/w(t) \sumk=0n [ pk(t) y(k) ](k) on [a,\infty),

is established. This condition is based on a recently proved generalized reciprocity principle for l and on the relationship between spectral properties of l and oscillation of a certain associated (2n-2)-order differential equation. An application to ''Euler-type'' fourth order operator is given.


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Last change: January 4, 1999. (c) Roman Hilscher