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A Schrödinger operator with a δ ′‐interaction on a Cantor set and Krein–Feller operators
Author(s) -
Albeverio Sergio,
Nizhnik Leonid
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310371
Subject(s) - mathematics , lebesgue measure , cantor set , operator (biology) , schrödinger's cat , measure (data warehouse) , spectrum (functional analysis) , set (abstract data type) , null set , pure mathematics , lebesgue integration , mathematical analysis , quantum mechanics , physics , biochemistry , chemistry , repressor , database , computer science , transcription factor , gene , programming language
A construction of a one‐dimensional Schrödinger operator that has an inner structure defined on a set of Lebesgue measure zero and an interaction given on such a set. General Krein–Feller operators are constructed and the spectrum of a Schrödinger operator with a δ ′‐interaction given on a Cantor set is studied. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)