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

  • A. M. Gomilko

Abstract

A bundle of differential operators L(λ),λC:L(λ)y(x)=y(4)(x)2λ2y(2)(x)+λ4y(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 yk(x),k=1,2,..., are the eigenfunctions of the bundle L(λ) corresponding to the eigenvalues λk, with λk>0.
Published
25.12.1993
How to Cite
Gomilko, A. M. “Expansion of a Bundle of Fourth-Order Differential Operators in a Part of Its Eigenfunctions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 12, Dec. 1993, pp. 1601–1612, https://umj.imath.kiev.ua/index.php/umj/article/view/5967.
Section
Research articles