Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions - Gomilko, A. M. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
A bundle of differential operators L(λ ),λ C:L(λ )y(x) = y^(4) (x) - 2λ ^2 y^(2) (x) + λ ^4 y(x),|x| 1,y( ± 1) = y′ ( ± 1) = 0, is considered. In various function spaces, we establish the facts about the expansions of a pair of functions f(x) and g(x) in the system {y_k (x), iλ_k y_k (x)|_k=1^ ∞, where y_k(x), k = 1,2,..., are the eigenfunctions of the bundle L (λ) corresponding to the eigenvalues λ_k, with λ_k > 0.