On Schrödinger's factorization method for Sturm-Liouville operators
1978 ◽
Vol 80
(1-2)
◽
pp. 67-84
◽
Keyword(s):
SynopsisWe consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequalityσd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.
2003 ◽
Vol 133
(4)
◽
pp. 747-758
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2021 ◽
2019 ◽
Vol 27
(4)
◽
pp. 501-509
◽
1994 ◽
Vol 116
(1)
◽
pp. 167-177
◽
2018 ◽
Keyword(s):