2019
Том 71
№ 11

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

Gomilko A. M.

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 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 $\Im λ_k > 0$.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1801-1814.

Citation Example: Gomilko A. M. Expansion of a bundle of fourth-order differential operators in a part of its eigenfunctions // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1601–1612.

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