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Differentiable perturbation of unbounded operators

Andreas Kriegl·Peter W. Michor
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Abstract

If $A(t)$ is a $C^{1,\al}$-curve of unbounded self-adjoint operators with compact resolvents and common domain of definition, then the eigenvalues can be parameterized $C^1$ in $t$. If $A$ is $C^\infty$ then the eigenvalues can be parameterized twice differentiable.

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Andreas Kriegl, Peter W. Michor. 2003-04-07. Differentiable perturbation of unbounded operators. https://arxiv.org/abs/math/0204060

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