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Self‐adjoint Sturm–Liouville problems with an infinite number of boundary conditions
Author(s) -
Zhao Yingchun,
Sun Jiong,
Zettl Anton
Publication year - 2016
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.201400415
Subject(s) - mathematics , hilbert space , sturm–liouville theory , interval (graph theory) , cover (algebra) , inner product space , space (punctuation) , boundary (topology) , connection (principal bundle) , mathematical analysis , pure mathematics , boundary value problem , self adjoint operator , combinatorics , geometry , mechanical engineering , linguistics , philosophy , engineering
We study Sturm–Liouville (SL) problems on an infinite number of intervals, adjacent endpoints are linked by means of boundary conditions, and characterize the conditions which determine self‐adjoint operators in a Hilbert space which is the direct sum of the spaces for each interval. These conditions can be regular or singular, separated or coupled. Furthermore, the inner products of the summand spaces may be multiples of the usual inner products with different spaces having different multiples. We also extend the GKN Theorem to cover the infinite number of intervals theory with modified inner products and discuss the connection between our characterization and the classical one with the usual inner products. Our results include the finite number of intervals case.