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Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1801–1814 | Cite as

Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions

  • A. M. Gomilko
Article

Abstract

A bundle of differential operators
$$\mathcal{L}(\lambda ),\lambda \in \mathbb{C}:\mathcal{L}(\lambda )y(x) = y^{(4)} (x) - 2\lambda ^2 y^{(2)} (x) + \lambda ^4 y(x),|x| \leqslant 1,y( \pm 1) = y\prime ( \pm 1) = 0,$$

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), 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.

Keywords

Differential Operator Function Space 
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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. M. Gomilko
    • 1
  1. 1.Institute of HydromechanicsUkrainian Academy of SciencesKiev

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