Abstract
A bundle of differential operators
is considered. In various function spaces, we establish the facts about the expansions of a pair of functionsf(x) andg(x) in the system {y k (x),iλ k y k (x)} ∞ k=1 , wherey k (x),k=1,2,..., are the eigenfunctions of the bundle\(\mathcal{L}\)(λ) corresponding to the eigenvalues λ k , with Im λ k >0.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1601–1612, December, 1993.
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Gomilko, A.M. Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions. Ukr Math J 45, 1801–1814 (1993). https://doi.org/10.1007/BF01061350
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DOI: https://doi.org/10.1007/BF01061350