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A note on the matrix Sturm‐Liouville operators with principal functions
Author(s) -
Yokus Nihal,
Coskun Nimet
Publication year - 2018
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.5383
Subject(s) - mathematics , sturm–liouville theory , invertible matrix , eigenvalues and eigenvectors , gravitational singularity , pure mathematics , operator (biology) , differential operator , matrix (chemical analysis) , matrix function , function (biology) , boundary value problem , mathematical analysis , symmetric matrix , chemistry , materials science , repressor , biology , composite material , biochemistry , physics , quantum mechanics , evolutionary biology , transcription factor , gene
In this study, we take under investigation principal functions corresponding to the eigenvalues and the spectral singularities of the Operator L generated in L 2 ( R + , E ) by the differential expression l ( y ) = − y ′ ′ + Q ( x ) y , x ∈ R + : = [ 0 , ∞ ) and the boundary condition ( A 0 + A 1 λ + A 2 λ 2 ) y ′ (0, λ ) − ( B 0 + B 1 λ + B 2 λ 2 ) y (0, λ ) = 0, where Q is a matrix‐valued function and A i , B i , i = 0,1,2 are non‐selfadjoint matrices also A 2 , B 2 are invertible.