Geodesic
Trace of Order~$(-1)$ for a String with Singular Weight
Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 197-215

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The Sturm–Liouville problem on a finite closed interval with potential and weight of first order of singularity is studied. Estimates for the $s$-numbers and eigenvalues of the corresponding integral operator are obtained. The spectral trace of first negative order is evaluated in terms of the integral kernel. The obtained theoretical results are illustrated by examples.
Keywords: spectral asymptotics, spectral trace.
Mots-clés : Sturm–Liouville problem 
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     author = {A. S. Ivanov and A. M. Savchuk},
     title = {Trace of {Order~}$(-1)$ for a {String} with {Singular} {Weight}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a3/}
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A. S. Ivanov; A. M. Savchuk. Trace of Order~$(-1)$ for a String with Singular Weight. Matematičeskie zametki, Tome 102 (2017) no. 2, pp. 197-215. http://geodesic.mathdoc.fr/item/MZM_2017_102_2_a3/