HILSCHER, Roman. Spectral properties of general self-adjoint, even order differential operators. Mathematica Slovaca. Bratislava: Slovak Academy of Sciences, 2000, vol. 50, No 2, p. 165-186, 21 pp. ISSN 0139-9918.
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Basic information
Original name Spectral properties of general self-adjoint, even order differential operators
Authors HILSCHER, Roman (203 Czech Republic, guarantor).
Edition Mathematica Slovaca, Bratislava, Slovak Academy of Sciences, 2000, 0139-9918.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Slovakia
Confidentiality degree is not subject to a state or trade secret
RIV identification code RIV/00216224:14310/00:00008154
Organization unit Faculty of Science
Keywords in English (non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution
Tags (non)oscillatory equation, Linear hamiltonian system, Principal solution, property BD, reciprocity principle
Changed by Changed by: prof. RNDr. Roman Šimon Hilscher, DSc., učo 1023. Changed: 10/9/2003 12:44.
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.
Links
GA201/96/0410, research and development projectName: Diferenciální a funkcionálně-diferenciální rovnice
Investor: Czech Science Foundation, Differential and functional - differential equations
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