Publication details

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

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Year of publication 2000
Type Article in Periodical
Magazine / Source Mathematica Slovaca
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords (non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution
Description 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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