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

• Date: 1993
• Main Authors: Gomilko, A. M., Гомилко, А. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5967
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 expan...