This article is cited in 11 papers

Eigenfunction Expansions Associated with One-Dimensional Periodic Differential Operators of Order $2n$

V. A. Tkachenko

Ben-Gurion University of the Negev

Abstract: We prove an explicit formula for spectral expansions in $L^2(\mathbb{R})$ generated by self-adjoint differential operators
$$ (-1)^n\frac{d^{2n}}{dx^{2n}}+\sum_{j=0}^{n-1}\frac{d^{j}}{dx^{j}}\, p_j(x)\frac{d^{j}}{dx^{j}}\,,\qquad p_j(x+\pi)=p_j(x),\quad x\in\mathbb{R}. $$


Keywords: differential operator, eigenfunction expansion, spectral matrix.

UDC: 517.983.35

Received: 15.05.2006

DOI: 10.4213/faa2853

 English version: Functional Analysis and Its Applications, 2007, 41:1, 54–72

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