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Fractional powers of the algebraic sum of normal operators. (English) Zbl 1092.47027
The author establishes sufficient conditions governing the following fact: if $$A$$ and $$B$$ are unbounded normal linear operators on a (complex) Hilbert space $$H$$, then for each $$\alpha \in (0,1)$$ ${D}(({\overline{A+B}})^{\alpha}) = {D}(A^{\alpha})\cap {D}(B^{\alpha})= {D}(({\overline{A+B}})^{*\alpha}),$ where $$\overline{A+B}$$ denotes the closure of the algebraic sum $$A+B$$ of $$A$$ and $$B$$. This result is applied to characterize the domains of fractional powers of a large class of the Hamiltonians with singular potentials arising in quantum mechanics through the study of the Schrödinger equation.

##### MSC:
 47B25 Linear symmetric and selfadjoint operators (unbounded) 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B44 Linear accretive operators, dissipative operators, etc.
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