One-dimensional Schr枚dinger operators with -interactions on Cantor-type sets

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• 作者：Jonathan Eckhardt^a ; ^{j.eckhardt@cs.cardiff.ac.uk" class="auth_mail} ; Aleksey Kostenko^b ; ^{duzer80@gmail.com" class="auth_mail} ; ^{Oleksiy.Kostenko@univie.ac.at" class="auth_mail} ; Mark Malamud^c ; ^{mmm@telenet.dn.ua" class="auth_mail} ; Gerald Teschl^b ; ^d ; ^{Gerald.Teschl@univie.ac.at" class="auth_mail} ;
• 关键词：primary ; 34L40 ; 81Q10 ; secondary ; 34L05 ; 34L20
• 刊名：Journal of Differential Equations
• 出版年：15 July 2014
• 年：2014
• 卷：257
• 期：2
• 页码：415-449
• 全文大小：440 K

文摘

We introduce a novel approach for defining a 未^′${未}^{\prime }$-interaction on a subset of the real line of Lebesgue measure zero which is based on Sturm–Liouville differential expression with measure coefficients. This enables us to establish basic spectral properties (e.g., self-adjointness, lower semiboundedness and spectral asymptotics) of Hamiltonians with 未^′${未}^{\prime }$-interactions concentrated on sets of complicated structures.