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A Spectrum Determined by Eigencurves
Author(s) -
Binding Paul,
Volkmer Hans
Publication year - 1999
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.19992020102
Subject(s) - mathematics , eigenfunction , spectrum (functional analysis) , hilbert space , operator (biology) , parameterized complexity , sturm–liouville theory , representation (politics) , mathematical analysis , boundary (topology) , space (punctuation) , pure mathematics , boundary value problem , self adjoint operator , mathematical physics , combinatorics , eigenvalues and eigenvectors , physics , quantum mechanics , biochemistry , chemistry , linguistics , philosophy , repressor , politics , political science , transcription factor , law , gene
This paper investigates the self‐adjoint operator ‐ ∂ 2 /∂x 2 + q(x, y ) in the Hilbert space L 2 (( a, b )× ( c,d )) subject to the boundary conditions z ( a,y ) = z ( b,y ) = 0. It is shown that the spectrum and spectral representation of A are determined by the eigencurves and eigenfunctions of the parameterized regular Sturm‐Liouville operator ‐ d 2 / dx 2 + q(x,y ).
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