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Eigenfunction expansions associated with one-dimensional periodic differential operators of order 2<Emphasis Type="Italic">n</Emphasis> |
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| Authors: | V Tkachenko |
| Institution: | (1) Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel |
| Abstract: | We prove an explicit formula for spectral expansions in L 2(?) generated by self-adjoint differential operators $( - 1)^n \frac{{d^{2n} }}{{dx^{2n} }} + \sum\limits_{j = 0}^{n - 1} {\frac{{d^j }}{{dx^j }}p_j (x)\frac{{d^j }}{{dx^j }}} ,p_j (x + \pi ) = p_j (x),x \in \mathbb{R}.$ |
| Keywords: | differential operator eigenfunction expansion spectral matrix |
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