The spectra of well-posed operators
1995 ◽
Vol 125
(6)
◽
pp. 1331-1348
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Keyword(s):
In this paper, the general ordinary quasidifferential expression M of nth order, with complex coefficients, and its formal adjoint M− are considered. It is shown in the case of two singular endpomts and when all solutions of the equation and the adjoint equation are in (the limit-circle case) that all well-posed extensions of the minimal operator T0(M) have resolvents which are Hilbert Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all of the standard essential spectra to be empty. These results extend those for the formally symmetric expression M studied in [1] and [14], and also extend those proved in [8] for one singular endpoint.
1980 ◽
Vol 86
(3-4)
◽
pp. 275-289
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Keyword(s):
2010 ◽
Vol 284
(2-3)
◽
pp. 342-354
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Keyword(s):
1945 ◽
Vol 12
(2)
◽
pp. 255-273
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1985 ◽
Vol 1
(3)
◽
pp. 225-230
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Keyword(s):
Keyword(s):