Das asymptotische verhalten der greenschen funktion N‐irregulaärer eigenwertprobleme mit zerfallenden randbedingungen

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.