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Das asymptotische verhalten der greenschen funktion N‐irregulaärer eigenwertprobleme mit zerfallenden randbedingungen
Author(s) -
Wolter M.,
Neunzert H.
Publication year - 1983
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.1670050122
Subject(s) - eigenfunction , mathematics , eigenvalues and eigenvectors , asymptotic expansion , function (biology) , mathematical analysis , boundary value problem , series (stratigraphy) , physics , quantum mechanics , evolutionary biology , biology , paleontology
We prove asymptotic estimates for the Green's function of N‐irregular eigenvalue problems My = λNγ with splitting boundary conditions. In contrast to the N‐regular case the Green's function G ( x ,ζ,λ) grows exponentially for |λ| → ∞ if x > ζ. These estimates are fundamental for the expansion of functions into a series of eigenfunctions of N‐irregular eigenvalue problems. In a subsequent paper it will be shown that this irregular behavior of G ( x ,ζ,λ) implies that only a very small class of functions can be expanded into a series of eigenfunctions of such problems.