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Spectral analysis of higher order differential operators with unbounded coefficients
Author(s) -
Behncke Horst,
Nyamwala Fredrick Oluoch
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910178
Subject(s) - mathematics , differential operator , spectral theorem , eigenvalues and eigenvectors , constant coefficients , operator theory , differential (mechanical device) , order (exchange) , spectral properties , unbounded operator , fourier integral operator , linear operators , pure mathematics , mathematical analysis , microlocal analysis , spectral analysis , approximation property , chemistry , physics , computational chemistry , banach space , finance , quantum mechanics , aerospace engineering , engineering , economics , bounded function , spectroscopy
Higher 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.