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The invariance of essential spectra of balslev-gamelin-fashian differential operators in the scale of lebesgue spaces

The invariance of essential spectra of balslev-gamelin-fashian differential operators in the... 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]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The invariance of essential spectra of balslev-gamelin-fashian differential operators in the scale of lebesgue spaces

Differential Equations , Volume 36 (8) – Nov 15, 2007

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/BF02754181
Publisher site
See Article on Publisher Site

Abstract

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].

Journal

Differential EquationsSpringer Journals

Published: Nov 15, 2007

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