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D. Edmunds, Des Evans (2018)
Spectral Theory and Differential OperatorsOxford Scholarship Online
E. Balslev, T. Gamelin (1964)
THE ESSENTIAL SPECTRUM OF A CLASS OF ORDINARY DIFFERENTIAL OPERATORSPacific Journal of Mathematics, 14
S. Goldberg (1966)
Unbounded linear operators : theory and applications
M. Schechter (1970)
The conjugate of a product of operatorsJournal of Functional Analysis, 6
W. Evans, M. Kwong, A. Zettl (1983)
Lower bounds for the spectrum of ordinary differential operatorsJournal of Differential Equations, 48
Differential Equations, Vol. 36, No. 8, 2000, pp. 1139-1145. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 8, 2000, pp. 1029-1036. Original Russian Text Copyright (~) 2000 by Erovenko. ORDINARY DIFFERENTIAL EQUATIONS The Invariance of Essential Spectra of Balslev-Gamelin-Fashian Differential Operators in the Scale of Lebesgue Spaces V. A. Erovenko Belarus State University, Belarus Received November 11, 1998 We consider spectral and semi-Fredholm properties of maximal and minimal Balslev-Gamelin- Fashian differential operators in the scale of Lebesgue spaces on the half-line and, by way of appli- cation, obtain exact formulas for various essential spectra and the spectrum of ordinary differential operators with polynomial coefficients whose order does not exceed the order of the corresponding derivative. Balslev and Gamelin [1, p. 771] investigated Fredholm properties of maximal differential operators generated by the Fashian differential expression of the form (mf)(t) = ~j~=o aj(t)f(3)(t), where ak(t) = O (tk), in the spaces LV(1, oc), 1 < p < r Various essential spectra of the max- imal and minimal Euler differential operators generated by the expression m with coefficients ak(t) = akt k in the spaces LP(1, co) and LP(0, 1), 1 < p < co, were given for the first time in [2].
Differential Equations – Springer Journals
Published: Nov 15, 2007
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