ASYMPTOTICS OF THE EIGENVALUES AND REGULARIZED TRACE OF THE FIRST-ORDER STURM–LIOUVILLE OPERATOR WITH δ-POTENTIAL

2016 ◽  
pp. 104-113
Author(s):  
Natal’ya Konechnaya ◽  
◽  
Tat’yana Safonova ◽  
Rena Tagirova
Keyword(s):  
Liouville Operator ◽  
Regularized Trace ◽  
First Order ◽  
Sturm Liouville ◽  
Asymptotics Of The Eigenvalues

On Schrödinger's factorization method for Sturm-Liouville operators

1978 ◽  
Vol 80 (1-2) ◽  
pp. 67-84 ◽  
Author(s):  
U.-W. Schmincke
Keyword(s):  
Discrete Spectrum ◽  
Liouville Operator ◽  
Differential Operators ◽  
Factorization Method ◽  
Friedrichs Extension ◽  
First Order ◽  
Sturm Liouville ◽  
Image Position ◽  
Special Case ◽  
Liouville Operators

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.

scholarly journals The formula for the regularized trace of the Sturm-Liouville operator with a logarithmic potential

2019 ◽  
Vol 50 (3) ◽  
pp. 269-280
Author(s):  
Khabir Kabirovich Ishkin ◽  
Leisan Gainullovna Valiullina
Keyword(s):  
Trace Formula ◽  
Liouville Operator ◽  
Logarithmic Potential ◽  
Regularized Trace ◽  
Sturm Liouville

We have obtained a regularized trace formula for the Sturm-Liouville operator on a semi-axis with a logarithmic potential.

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