Stone-regul�re Eigenwertprobleme

Boundary Eigenvalue Problems for Differential Equations Nη=λPη with λ-Polynomial Boundary Conditions

“…This theorem follows from the matrix version of a well known theorem on asymptotic fundamental systems for differential equations N'=*P' going back to W. Eberhard and G. Freiling [15], and to R. Mennicken and M. Mo ller [35,36]. It follows from the respective Theorem 2.2 in [57] if we set …”

Sampling expansions associated with Kamke problems

“…The following theorem and some of its generalizations have been proved in [18], [32], [38], [53][54]. …”

“…This work has been continued and generalized in the 60 ies by Schäfke and Schneider [43][44][45][46], who introduced the class of S-hermitian problems, and later on by Dijksma, Langer and de Snoo [13][14]. A detailed investigation of non self adjoint BVPs of the form (1.18)-(1.19) was initiated by Eberhard and Freiling in the 70 ies , [15][16][17][18], [21], who proved asymptotic estimates for fundamental systems of solutions of (1.18) when |λ| −→ ∞. These estimates are obtained using the contour integration (Cauchy) method, which generalizes the methods used by Birkhoff [5][6], Stone [50], Tamarkin [51] and many others in the case P (y) = y.…”

“…From Theorem 2.1 it follows that, see [18] or [54, Sect. 1.2], for ρ ∈ S ν and λ = −ρ n , the characteristic determinant…”

“…See [18,49]. From now on we assume that problem (1.18)-(1.19) and its adjoint, which will be defined below, are strongly regular.…”