Spectral analysis of higher order differential operators with unbounded coefficients
Copyright policy )Spectral analysis of higher order differential operators with unbounded coefficients
AbstractHigher even order linear differential operators with unbounded coefficients are studied. For these operators the eigenvalues of the characteristic polynomials fall into distinct classes or clusters. Consequently the spectral properties, deficiency indices and spectra, of the underlying differential operators are superpositions of the contributions from the individual clusters. These results are based on a quantitative improvement of Levinson's Theorem. Our methods will also be applicable to other classes of linear differential operators.
- Osnabrück University Germany
- Maseno University Kenya
absolutely continuous spectrum, dichotomy condition, power coefficients, General theory of ordinary differential operators, diagonalization, General spectral theory of ordinary differential operators, spectrum, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, differential operator, asymptotic integration, deficiency index, asymptotic integration, deficiency index
absolutely continuous spectrum, dichotomy condition, power coefficients, General theory of ordinary differential operators, diagonalization, General spectral theory of ordinary differential operators, spectrum, Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators, differential operator, asymptotic integration, deficiency index, asymptotic integration, deficiency index
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