2013
DOI: 10.1007/s11854-013-0018-x
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Sturm-Liouville operators with measure-valued coefficients

Abstract: Abstract. We give a comprehensive treatment of Sturm-Liouville operators whose coefficients are measures including a full discussion of self-adjoint extensions and boundary conditions, resolvents, and Weyl-Titchmarsh-Kodaira theory. We avoid previous technical restrictions and, at the same time, extend all results to a larger class of operators. Our operators include classical SturmLiouville operators, Sturm-Liouville operators with (local and non-local) δ and δ ′ interactions or transmission conditions as wel… Show more

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Cited by 66 publications
(127 citation statements)
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“…Existence and uniqueness follows readily from [49 [24,Theorem A.2]). An inspection of the fixed-point iteration in [49] shows that real-valued data yields real-valued solutions.…”
Section: )mentioning
confidence: 99%
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“…Existence and uniqueness follows readily from [49 [24,Theorem A.2]). An inspection of the fixed-point iteration in [49] shows that real-valued data yields real-valued solutions.…”
Section: )mentioning
confidence: 99%
“…The claim follows from the fixed-point iteration which converges locally uniformly in z ∈ C (see [44, §1.3], [4, Lemma 1.5], [24,Theorem A.5]). …”
Section: )mentioning
confidence: 99%
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“…Note that in the cited sources all considerations involve asymptotics at the point at infinity, so there should be a coordinate change 1/x = t in Eq. (6) first. See also the treatment in the paper by Bühring [1].…”
Section: Remarkmentioning
confidence: 99%
“…[8,9,14,15,19]. Finally, we want to mention that generalised Titchmarsh-Weyl theory has also been extended to Sturm-Liouville operators with distributional and measure coefficients as well as to the one-dimensional Dirac operator and Jacobi operators, [2,[5][6][7]]. …”
Section: Introductionmentioning
confidence: 99%