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The counting function for a λ–rational Sturm–Liouville problem
Author(s) -
Greenberg Leon,
Marletta Marco
Publication year - 2003
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.200310059
Subject(s) - mathematics , essential spectrum , eigenvalues and eigenvectors , oscillation (cell signaling) , spectrum (functional analysis) , transformation (genetics) , mathematical analysis , pure mathematics , physics , biochemistry , genetics , chemistry , quantum mechanics , gene , biology
We develop an oscillation theory for an equation of Hain–Lüst type, valid both outside and inside the essential spectrum. The results proved allow us to locate eigenvalues in the essential spectrum or resonances close to the essential spectrum. The numerical implementation of the oscillation theory requires a regularizing transformation of Niessen and Zettl.