Geodesic
Eigenfunction Expansions Associated with One-Dimensional Periodic Differential Operators of Order~$2n$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 66-89.

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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
Mots-clés : spectral matrix. 
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V. A. Tkachenko. Eigenfunction Expansions Associated with One-Dimensional Periodic Differential Operators of Order~$2n$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 1, pp. 66-89. http://geodesic.mathdoc.fr/item/FAA_2007_41_1_a4/

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