Many parameter Hoelder perturbation of unbounded operators

Details Many parameter Hoelder perturbation of unbounded operators Many parameter Hoelder perturbation of unbounded operators

2006-11-16

arxiv.org/abs/math/0611506v2

Mathematics

Functional Analysis

LaTeX, 4 pages; The result is generalized from Lipschitz to Hoelder. Title changed

Scientific paper

If $u\mapsto A(u)$ is a $C^{0,\alpha}$-mapping, for $0< \alpha \le 1$, having
as values unbounded self-adjoint operators with compact resolvents and common
domain of definition, parametrized by $u$ in an (even infinite dimensional)
space, then any continuous (in $u$) arrangement of the eigenvalues of $A(u)$ is
indeed $C^{0,\alpha}$ in $u$.

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