Eigenfunction expansions associated with 1d periodic differential operators of order $2n$

V. Tkachenko

Eigenfunction expansions associated with 1d periodic differential operators of order $2n$

Spectral Theory 2007-05-23 v1 Functional Analysis

Authors: V. Tkachenko

Abstract

We prove an explicit formula for the spectral expansions in $L^2(\R)$ generated by selfadjoint differential operators $(-1)^n\frac{d^{2n}}{dx^{2n}}+\sum\limits_{j=0}^{n-1}\frac{d^{j}}{dx^{j}} p_j(x)\frac{d^{j}}{dx^{j}},\quad p_j(x+\pi)=p_j(x),\quad x\in\R.$

Keywords

spectral theory

Cite

@article{arxiv.math/0606339,
  title  = {Eigenfunction expansions associated with 1d periodic differential operators of order $2n$},
  author = {V. Tkachenko},
  journal= {arXiv preprint arXiv:math/0606339},
  year   = {2007}
}

Comments

25 pages

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