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Sturm‐Liouville eigenvalue problems on networks
Author(s) -
von Below Joachim
Publication year - 1988
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670100404
Subject(s) - eigenfunction , mathematics , eigenvalues and eigenvectors , hermitian matrix , divide and conquer eigenvalue algorithm , sturm–liouville theory , order (exchange) , mathematical analysis , pure mathematics , boundary value problem , physics , economics , finance , quantum mechanics
The description of heat conduction on ramified wires, for instance, leads to a Sturm‐Liouville eigenvalue problem on a network. It is shown that these problems are special canonical eigenvalue problems in the sense of Hölder, and therefore they can be investigated within the theory of S ‐Hermitian eigenvalue problems. In particular, Wielandt's expansion theorem can be applied in order to obtain eigenfunction expansions.